# Contemporary Philosophies and Social Theories

## Postmodernism

### Learning Objectives

By the end of this section, you will be able to:
1. Outline the main tenets of postmodernism.
2. Analyze structuralist theories in psychology and linguistics.
3. Evaluate the post-structuralist response to structuralism.
4. Explain concepts central to the thought of Derrida, Nietzsche, and Foucault.
Many modern scholars embraced the idea that the world operates according to a set of overarching universal structures. This view proposes that as we continue to progress in terms of technological, scientific, intellectual, and social advancements, we come closer to discovering universal truths about these structures. This view of progression toward truth gave rise to a school of thought known as structuralism, which is pervasive in many academic fields of study, as discussed below. Postmodernism departs from this way of thinking in rejecting these ideas and contending that there exists no one reality that we can be certain of and no absolute truth.

### Structuralism and Post-structuralism

The philosophical battle over whether there is one nonnegotiable reality took shape in conversations around structuralism and post-structuralism. Structuralists historically looked to verbal language and mathematics to show that symbols cannot refer to just anything we want them to refer to. For example, most people would say it is ridiculous to use the word car to refer to a dog. Rather, language and mathematics are universal systems of communication emerging from a universal structure of things. This claim sounds similar to Platonic idealism, in which the structures that ground our world are understood as intangible “forms.”
Post-structuralists argue that universal structures are abstract ideas that cannot be proven to exist. They contend that structuralists are mistaken in their understanding of the internal workings of language—or any system—as unmediated (or not influenced by the outside world). This mistake, they argue, had misled people into believing in a universal structure of things. Post-structuralism suggests that the meaning of things is in perpetual authorship, or is always being created and recreated. Post-structuralists dispute the claim that any universal system of relations exists. Rather, they argue that anything presented as a universal system is in fact the product of human imaginations and almost certainly reinforced by the power dynamics of a society.
One clear example of the post-structuralist critique of structuralism can be found in the debate over psychoanalysis.

### Freud’s Structuralism in Psychology

The theory of psychoanalysis is based on the idea that all humans have suppressed elements of their unconscious minds and that these elements will liberate them if they are confronted. This idea was proposed and developed by Austrian neurologist Sigmund Freud (1856–1939). For Freud, psychoanalysis was not only a theory but also a method, which he used to free his patients from challenges such as depression and anxiety. In Freud’s early thinking, the “unconscious” was defined as the realm in which feelings, thoughts, urges, and memories that exist outside of consciousness reside. These elements of the unconscious were understood to set the stage for conscious experience and influence the human automatically (Westen 1999). Freud later abandoned the use of the word unconscious (Carlson et al. 2010, 453), shifting instead to three separate terms: id, referring to human instincts; superego, indicating the enforcer of societal conventions such as cultural norms and ethics (Schacter, Gilbert, and Wegner 2011, 481); and ego, describing the conscious part of human thought. With these three terms, Freud proposed a universal structure of the mind.

### Post-structuralist and Feminist Critiques of Psychoanalysis

Post-structuralists point out that Freud’s ideas about psychoanalysis and universal structures of the mind cannot be proven. The subconscious foundations on which psychoanalysis is grounded simply cannot be observed. Some have argued that there is no substantive difference between the claims of psychoanalysts and those of shamans or other practitioners of methods of healing not grounded in empirical methods (Torrey 1986). French philosopher Gilles Deleuze (1925–1995) and French psychoanalyst Felix Guattari (1930–1992) took an even harsher approach, presenting psychoanalysis as a means of reinforcing oppressive state control.
Belgian philosopher Luce Irigaray (b. 1930) and others have criticized Freud’s ideas from a feminist perspective, accusing psychoanalysts of excluding women from their theories. In this view, psychoanalysis is based on a patriarchal understanding. Those taking this view point out that Freud made a number of patriarchal claims, including that sexuality and subjectivity are inseparably connected, and that he viewed women as problematic throughout his life (Zakin 2011). Yet many psychoanalytic feminists express a critical appreciation for Freud, utilizing what they find valuable in his theories and ignoring other aspects.

### Ferdinand de Saussure and the Structure of Linguistics

Along with US pragmatist C. S. Pierce (1839–1914), Swiss philosopher, linguist, and semiotician Ferdinand de Saussure (1857–1913) was responsible for creating a system of linguistic analysis known as semiotics. Semiotics is an analysis of how meaning is created through symbols, both linguistic and nonlinguistic. One of the foundational tenets of Saussure’s linguistic theory is the idea that language has both an abstract (langue) component and an experiential (parole) component, what we hear or see when it is used every day. A word alludes to an intangible essence represented by a sound or collection of visible symbols (Fendler 2010). This audible or visual expression has a distinct life from that which it represents. Language is a system that functions according to certain rules, which allow for some things but not others. For example, we can’t say a person is walking and standing still at the same time (Nöth 1990). As an audible or visual expression, however, language is also a product of society. For example, the word dope, which conventionally meant narcotics, has also come to signify something that is well-done. Saussure held that there were structural laws that define how linguistic signification operated; the semiotics of Saussure and Pierce were the means of discovering these laws. Semiotics became a cornerstone of structuralism.

### Wittgenstein and the Linguistic Turn

Structuralism was accompanied by what is known in philosophy as the linguistic turn. The term linguistic turn comes from Austrian philosopher Gustav Bergmann (1906–1987). It refers to philosophical movements in the Anglophone world starting in the early 20th century that privileged verifiable statements over statements that could not be verified. Since the statement “I can see clearly now” could be verified by a vision test, it would have more value than the statement “God exists,” which is not verifiable (Rorty 1991, 50).
The view that language has internal continuity was championed by the early work of Austrian philosopher Ludwig Wittgenstein (1889–1951) but rejected in his later work. In later works, such as Philosophical Investigations, Wittgenstein concludes that language is verifiable only within its particular context. For example, the claim “God exists” may not be verifiable for an adherent of analytic philosophy (a term for the branch of philosophy concerned with statements that can be proved to be logically possible through analysis). However, the claim might be verifiable for a person who has had an experience with a particular deity or deities, as their very experience is the proof.

### Key Post-structuralist Ideas about Self and Text

Associated with the thought of French philosophers Michel Foucault (1926–1984), Gilles Deleuze (1925–1995), and Roland Barthes (1915–1980) and US philosophers Alfred North Whitehead (1861–1947) and Judith Butler (b. 1956), among others, post-structuralism proposes new ideas about our understanding of the self and our interpretations of texts. Post-structuralism proposes that there is no such thing as a preexistent human “self” outside of its construction by society; what we call the “self” is a confluence of geographical region of birth, upbringing, social pressure, political issues, and other situational circumstances. For the post-structuralist, however, there is an experiencing entity perpetually in process, and that experiencing entity cannot be constricted to the boundaries of what we think of as the “self.” Similarly emphasizing context, post-structuralists argue that the meaning intended by the author of a text is secondary to the meaning that the audience derives from their encounter with the text and that a variety of interpretations of a text are needed, even if the interpretations that are generated are conflicting.

### Deconstruction

Closely related to post-structuralism is deconstruction. Accredited to Algerian-born French philosopher Jacques Derrida (1930–2004), deconstruction aims to analyze a text to discover that which made it what it was. Derrida rejected the structuralist approach to textual analysis. In the structuralist framework, there was a focus on how a text fits into a larger framework of linguistic meaning and signifying (Barry 2002, 40). Derrida, among others, held that these structures were as arbitrary as other facets of language, such as the arbitrary decision to use “tree” to refer to a large plant with a bark, trunk, and leaves when we could have called it a “cell phone” and have procured the same symbolic use (Thiselton 2009). Derrida asserted that texts do not have a definitive meaning but rather that there are several possible and plausible interpretations. His argument was based on the assertion that interpretation could not occur in isolation. While Derrida did not assert that all meanings were acceptable, he did question why certain interpretations were held as more correct than others (Thiselton 2009).

### Deconstruction is Auto-deconstruction

Derrida observed that social relations, which have come about through centuries of human evolution, assign meanings to things and our experience of things (Derrida 1997). Deconstruction hinged on what Derrida called “différance,” the separation between the ways a thing can be conceptualized and the ways a thing can be experienced. For example, the experience that we name the “human” is not fully containable through our attempts to define the concept. However, in our reference to the many competing notions of “human,” we have (perhaps unknowingly) artificially demarcated the experience, creating the appearance of the “human” as something with an essential identity.
To deconstruct a concept is to strip meaning from its supporting layers in order to make clear its complexity and instability. Derrida’s idea of différance is an integral part of “auto-deconstruction,” or the process by which deconstruction happens automatically (without intentional philosophical reflection). Auto-deconstruction is always present, but the human is not always attuned to see how things we see as definitive are deconstructing right before us. Auto-deconstruction could be thought of in terms of something as simple as the elements that constitute a chair. If we think about how the chair is made up, we might begin to lose sight of the idea of “chair” and begin to see it in terms of color, material, height, length, width, contrast to other objects in the room in which it resides, etc. Whether or not we focus on the confluence of things that make up the event of the chair, this tension of différance is what provides the perception of “chair” (Derrida 1997).

### Ethics in Post-structuralism

### Nietzsche’s Genealogy

When German philosopher Friedrich Nietzsche (1844–1900) famously declared that “God is dead,” he rejected God as a basis for morality and asserted that there is no longer (and never was) any ground for morality other than the human. The removal of the notion of sure foundations for ethical behavior and human meaning can stir a sense of anxiety, a fear of living without a place of certainty (Warnock 1978). This fear and anxiety inform the existential notion of the “absurd,” which is simply another way of stating that the only meaning the world has is the meaning that we give it (Crowell 2003). In this motion away from objective assertions of truth, one comes to what Nietzsche calls “the abyss,” or the world without the absolute logical structures and norms that provide meaning. The abyss is the world where nothing has universal meaning; instead, everything that was once previously determined and agreed upon is subject to individual human interpretation. Without the structures of fixed ethical mandates, the world can seem a perpetual abyss of meaninglessness.
Although Nietzsche lived prior to Derrida, he engaged in a type of deconstruction that he referred to as genealogy. In On the Genealogy of Morality, Nietzsche traces the meaning of present morals to their historical origins. For example, Nietzsche argued that the concepts we refer to as “good” and “evil” were formed in history through the linguistic transformation of the terms “nobility” and “underclass” (Nietzsche 2007, 147–148). Nietzsche held that the upper classes at one time were thought to be “noble,” having characteristics that the lower classes were envious or and would want to emulate. Therefore, “noble” was considered not an ethical “good” but a practical “good.” A person simply had a better life if they were part of the ruling class. Over time, the concept of “noble” took on a more ideal meaning, and the practical characteristics (e.g., reputation, access to resources, influence, etc.) became abstract virtues. Because the lower classes were envious of the upper classes, they found a theoretical framework to subvert the power of the nobility: Judeo-Christian philosophy. In Judeo-Christian philosophy, the “good” is no longer just a synonym for the nobility but a spiritual virtue and is represented by powerlessness. “Evil” is represented by strength and is a spiritual vice. Nietzsche views this reversal as one of the most tragic and dangerous tricks to happen to the human species. In his view, this system of created morality allows the weak to stifle the power of the strong and slow the progress of humanity.

### Foucault on Power and Knowledge

For French philosopher Michel Foucault (1926–1984), “power” at the base level is the impetus that urges one to commit any action (Lynch 2011, 19). Foucault claimed that power has been misunderstood; it has traditionally been understood as residing in a person or group, but it really is a network that exists everywhere. Because power is inescapable, everyone participates in it, with some winning and others losing.
Foucault contended that power affects the production of knowledge. He argued that Nietzsche’s process of genealogy exposed the shameful origins of practices and ideas that some societies have come to hold as “natural” and “metaphysically structural,” such as the inferiority of woman or the justification of slavery. For Foucault, these and other systems aren’t just the way things are but are the way things have been developed to be by the powerful, for their own benefit. The disruptions promoted by critical theory are viewed as insurrections against accepted histories—disruptions that largely deal with a reimagining of how we know what we know—and understood as a weapon against oppression.

### Political Movements Informed by Critical Theory

Although critical theory can seem highly abstract, it has inspired and informed concrete political movements in the 20th and 21st centuries. This section examines two of these, critical race theory and radical democracy.

### Critical Race Theory

One of the most controversial applications of critical theory concerns its study of race. Critical race theory approaches the concept of race as a social construct and examines how race has been defined by the power structure. Within this understanding, “Whiteness” is viewed as an invented concept that institutionalizes racism and needs to be dismantled. Critical race theorists trace the idea of “Whiteness” to the late 15th century, when it began to be used to justify the dehumanization and restructuring of civilizations in the Americas by Britain, Spain, France, Germany, and Belgium. As these colonizing nations established new societies on these continents, racism was built into their institutions. Thus, for example, critical race theorists argue that racism not as an anomaly but a characteristic of the American legal system. Ian Haney López’s White by Law: The Legal Construction of Race argued that racial norms in the United States are background assumptions that are legally supported and that impact the success of those socially defined by them. Critical race theory views the institutions of our society as replicating racial inequality.
The idea of institutionalized racism is not unique to critical race theory. Empirical studies, such as those carried out by W. E. B. Du Bois, have outlined the structure of institutionalized racism within communities. Critical race theories are unique in that they do not see policies that arise from these empirical studies as a solution because these policies, they argue, arise within a power structure that determines what we accept as knowledge. Instead, critical race theorists, like other branches of critical theory, turn to the philosopher, the teacher, or the student to relinquish their role as neutral observers and challenge the power structure and social institutions through dialog. Critics of this approach—and other critical theory approaches to education—worry that these programs seek to indoctrinate students in a manner that bears too close a resemblance to Maoist “self-criticism” campaigns.

### Radical Democracy

“Radical democracy” can be defined as a mode of thought that allows for political difference to remain in tension and challenges both liberal and conservative ideas about government and society. According to radical democracy, the expectation of uniform belief among a society or portion of a society is opposed to the expressed and implied tenets of democracy (Kahn and Kellner 2007). If one wants freedom and equality, then disparate opinions must be allowed in the marketplace of ideas.
One strand of radical democracy is associated with Habermas’s notion of deliberation as found in communicative action. Habermas argued for deliberation, not the normalizing of ideas through peer pressure and governmental influence, as a way in which ideological conflicts can be solved. Though Habermas admitted that different contexts will quite naturally disagree over important matters, the process of deliberation was viewed as making fruitful dialogue between those with opposing viewpoints possible (Olson [2011] 2014). Another type of radical democracy drew heavily on Marxist thought, asserting that radical democracy should not be based on the rational conclusions of individuals but grounded in the needs of the community.

###

Within the postmodernism perspective, there is no absolute truth, and there are multiple right ways of belief. The postmodern view challenges the intellectual faith born in modernity that humanity might someday come closer to discovering universal truths.
The tension between structuralism and post-structuralism parallels the tension between modernity and postmodernity. Ferdinand de Saussure advanced a theory in which meaning was embedded within a linguistic structure but the meaning itself is expressed through multiple mechanisms. With the so-called linguistic turn in philosophy, a challenge to the existence of universal systems (structures) was launched. As noted, three post-structuralist themes were: 1) the self itself is not static but a confluence of various forces, 2) the meaning of the author was secondary to the meaning derived from the audience, and 3) interpretations, even if conflicting, were necessarily plural. Derrida’s notion of deconstruction, of the need to consider the meaning accepted and the meaning obscured, followed intellectually from post-structuralism. If we deconstruct meaning, we work toward understanding the greater reasons surrounding why some interpretations were privileged and others rejected.
A “genealogy” is the historical map that traces the past origins of present meanings. Nietzsche and his radical historicism used genealogies to draw meanings in a world thought of a void of objective meanings. Michel Foucault argued that tracing genealogies can help us expose shameful origins of practices and ideologies that foster oppression. Foucault sought to expose when power was used to oppress and when it was used to harm. Knowledge, argued Foucault, once freed from oppressive conventions, ought to be used to develop the self.

###

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# Introduction: The Nature of Science and Physics

## Introduction to Science and the Realm of Physics, Physical Quantities, and Units

What is your first reaction when you hear the word “physics”? Did you imagine working through difficult equations or memorizing formulas that seem to have no real use in life outside the physics classroom? Many people come to the subject of physics with a bit of fear. But as you begin your exploration of this broad-ranging subject, you may soon come to realize that physics plays a much larger role in your life than you first thought, no matter your life goals or career choice.
Consider the Veil Nebula, a cloud of heated dust and gas located about 2,400 light years from Earth (a light year is the distance light travels in one year, or approximately 9.5 trillion kilometers). The unique structure is the ongoing result of a supernova that occurred 8,000 years ago. The shock wave from the explosion is colliding with a cloud of gas and dust, creating the rope-like filaments and sheet-like appearance. Scientists compare newer images, such as the one above, with detailed images taken by the Hubble Space Telescope in 1997 in order to understand nebula expansion and other properties of astronomical objects. The forces that cause the supernova remnant to act as it does are the same forces we contend with here on Earth, whether we are planning to send a rocket into space or simply heating a new home. Although the scale is much different, the interaction of gasses in the Veil Nebula resembles those on Earth; and the vibrant color combinations are created by the familiar glows of hydrogen, sulfur, oxygen, and similar elements that make up everything we know. Tonight, take a moment to look up at the stars. The forces out there are the same as the ones here on Earth. Through a study of physics, you may gain a greater understanding of the interconnectedness of everything we can see and know in this universe.
Humans have created and manufactured millions of different objects over the history of our species. Successive technological periods (often referred to as the Stone Age, the Bronze Age, the Iron Age, and so on) were marked by our knowledge of the physical properties of certain materials and our ability to manipulate them. This knowledge all stems from physics, whether it's the way a rock would flake when constructing a spear point, the effect of integrating carbon with iron in South Indian and Sri Lankan furnaces to create the earliest high-quality steel, or the proper way to combine perfectly ground and polished pieces of glass to create optical instruments. Our current technological age, the Information Age, builds on all that knowledge and can be traced to critical innovations made by people from all backgrounds working together. Mohamed M. Atalla and Dawon Kahng, for example, invented the MOSFET (metal-oxide-semiconductor field-effect transistor). Although unknown to most people, this tiny device, created in 1959 by an Egyptian-born scientist and Korean-born scientist working in a lab in New Jersey, is the basis for modern electronics. More MOSFETs have been produced than any other object in human history. They are used in computers, smart phones, microwave ovens, automotive controls, medical instruments, and nearly every other electronic device.
Next, think about the most exciting modern technologies that you have heard about in the news, such as trains that levitate above tracks, “invisibility cloaks” that bend light around them, and microscopic robots that fight cancer cells in our bodies. All of these groundbreaking advancements, commonplace or unbelievable, rely on the principles of physics. Aside from playing a significant role in technology, professionals such as engineers, pilots, physicians, physical therapists, electricians, and computer programmers apply physics concepts in their daily work. For example, a pilot must understand how wind forces affect a flight path and a physical therapist must understand how the muscles in the body experience forces as they move and bend. As you will learn in this text, physics principles are propelling new, exciting technologies, and these principles are applied in a wide range of careers.
In this text, you will begin to explore the history of the formal study of physics, beginning with natural philosophy and the ancient thinkers from the Middle East and the Mediterranean, and leading up through a review of Sir Isaac Newton and the laws of physics that bear his name. You will also be introduced to the standards scientists use when they study physical quantities and the interrelated system of measurements most of the scientific community uses to communicate in a single mathematical language. Finally, you will study the limits of our ability to be accurate and precise, and the reasons scientists go to painstaking lengths to be as clear as possible regarding their own limitations.


# Introduction: The Nature of Science and Physics

## Physics: An Introduction

### Learning Objectives

By the end of this section, you will be able to:
1. Explain the difference between a principle and a law.

2. Explain the difference between a model and a theory.

The physical universe is enormously complex in its detail. Every day, each of us observes a great variety of objects and phenomena. Over the centuries, the curiosity of the human race has led us collectively to explore and catalog a tremendous wealth of information. From the flight of birds to the colors of flowers, from lightning to gravity, from quarks to clusters of galaxies, from the flow of time to the mystery of the creation of the universe, we have asked questions and assembled huge arrays of facts. In the face of all these details, we have discovered that a surprisingly small and unified set of physical laws can explain what we observe. As humans, we make generalizations and seek order. We have found that nature is remarkably cooperative—it exhibits the underlying order and simplicity we so value.
It is the underlying order of nature that makes science in general, and physics in particular, so enjoyable to study. For example, what do a bag of chips and a car battery have in common? Both contain energy that can be converted to other forms. The law of conservation of energy (which says that energy can change form but is never lost) ties together such topics as food calories, batteries, heat, light, and watch springs. Understanding this law makes it easier to learn about the various forms energy takes and how they relate to one another. Apparently unrelated topics are connected through broadly applicable physical laws, permitting an understanding beyond just the memorization of lists of facts.
The unifying aspect of physical laws and the basic simplicity of nature form the underlying themes of this text. In learning to apply these laws, you will, of course, study the most important topics in physics. More importantly, you will gain analytical abilities that will enable you to apply these laws far beyond the scope of what can be included in a single book. These analytical skills will help you to excel academically, and they will also help you to think critically in any professional career you choose to pursue. This module discusses the realm of physics (to define what physics is), some applications of physics (to illustrate its relevance to other disciplines), and more precisely what constitutes a physical law (to illuminate the importance of experimentation to theory).

### Science and the Realm of Physics

Science consists of the theories and laws that are the general truths of nature as well as the body of knowledge they encompass. Scientists are continually trying to expand this body of knowledge and to perfect the expression of the laws that describe it. Physics is concerned with describing the interactions of energy, matter, space, and time, and it is especially interested in what fundamental mechanisms underlie every phenomenon. The concern for describing the basic phenomena in nature essentially defines the realm of physics.
Physics aims to describe the function of everything around us, from the movement of tiny charged particles to the motion of people, cars, and spaceships. In fact, almost everything around you can be described quite accurately by the laws of physics. Consider a smart phone (). Physics describes how electricity interacts with the various circuits inside the device. This knowledge helps engineers select the appropriate materials and circuit layout when building the smart phone. Next, consider a GPS system. Physics describes the relationship between the speed of an object, the distance over which it travels, and the time it takes to travel that distance. GPS relies on precise calculations that account for variations in the Earth's landscapes, the exact distance between orbiting satellites, and even the effect of a complex occurrence of time dilation. Most of these calculations are founded on algorithms developed by Gladys West, a mathematician and computer scientist who programmed the first computers capable of highly accurate remote sensing and positioning. When you use a GPS device, it utilizes these algorithms to recognize where you are and how your position relates to other objects on Earth.

### Applications of Physics

You need not be a scientist to use physics. On the contrary, knowledge of physics is useful in everyday situations as well as in nonscientific professions. It can help you understand how microwave ovens work, why metals should not be put into them, and why they might affect pacemakers. (See  and .) Physics allows you to understand the hazards of radiation and rationally evaluate these hazards more easily. Physics also explains the reason why a black car radiator helps remove heat in a car engine, and it explains why a white roof helps keep the inside of a house cool. Similarly, the operation of a car’s ignition system as well as the transmission of electrical signals through our body’s nervous system are much easier to understand when you think about them in terms of basic physics.
Physics is the foundation of many important disciplines and contributes directly to others. Chemistry, for example—since it deals with the interactions of atoms and molecules—is rooted in atomic and molecular physics. Most branches of engineering are applied physics. In architecture, physics is at the heart of structural stability, and is involved in the acoustics, heating, lighting, and cooling of buildings. Parts of geology rely heavily on physics, such as radioactive dating of rocks, earthquake analysis, and heat transfer in the Earth. Some disciplines, such as biophysics and geophysics, are hybrids of physics and other disciplines.
Physics has many applications in the biological sciences. On the microscopic level, it helps describe the properties of cell walls and cell membranes ( and ). On the macroscopic level, it can explain the heat, work, and power associated with the human body. Physics is involved in medical diagnostics, such as x-rays, magnetic resonance imaging (MRI), and ultrasonic blood flow measurements. Medical therapy sometimes directly involves physics; for example, cancer radiotherapy uses ionizing radiation. Physics can also explain sensory phenomena, such as how musical instruments make sound, how the eye detects color, and how lasers can transmit information.
It is not necessary to formally study all applications of physics. What is most useful is knowledge of the basic laws of physics and a skill in the analytical methods for applying them. The study of physics also can improve your problem-solving skills. Furthermore, physics has retained the most basic aspects of science, so it is used by all of the sciences, and the study of physics makes other sciences easier to understand.

### Models, Theories, and Laws; The Role of Experimentation

The laws of nature are concise descriptions of the universe around us; they are human statements of the underlying laws or rules that all natural processes follow. Such laws are intrinsic to the universe; humans did not create them and so cannot change them. We can only discover and understand them. Their discovery is a very human endeavor, with all the elements of mystery, imagination, struggle, triumph, and disappointment inherent in any creative effort. (See  and .) The cornerstone of discovering natural laws is observation; science must describe the universe as it is, not as we may imagine it to be.
We all are curious to some extent. We look around, make generalizations, and try to understand what we see—for example, we look up and wonder whether one type of cloud signals an oncoming storm. As we become serious about exploring nature, we become more organized and formal in collecting and analyzing data. We attempt greater precision, perform controlled experiments (if we can), and write down ideas about how the data may be organized and unified. We then formulate models, theories, and laws based on the data we have collected and analyzed to generalize and communicate the results of these experiments.
A model is a representation of something that is often too difficult (or impossible) to display directly. While a model is justified with experimental proof, it is only accurate under limited situations. An example is the planetary model of the atom in which electrons are pictured as orbiting the nucleus, analogous to the way planets orbit the Sun. (See .) We cannot observe electron orbits directly, but the mental image helps explain the observations we can make, such as the emission of light from hot gases (atomic spectra). Physicists use models for a variety of purposes. For example, models can help physicists analyze a scenario and perform a calculation, or they can be used to represent a situation in the form of a computer simulation. A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers. Some theories include models to help visualize phenomena, whereas others do not. Newton’s theory of gravity, for example, does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on the other hand, is a model in which a gas is viewed as being composed of atoms and molecules. Atoms and molecules are too small to be observed directly with our senses—thus, we picture them mentally to understand what our instruments tell us about the behavior of gases.
A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. Often, a law can be expressed in the form of a single mathematical equation. Laws and theories are similar in that they are both scientific statements that result from a tested hypothesis and are supported by scientific evidence. However, the designation law is reserved for a concise and very general statement that describes phenomena in nature, such as the law that energy is conserved during any process, or Newton’s second law of motion, which relates force, mass, and acceleration by the simple equation . A theory, in contrast, is a less concise statement of observed phenomena. For example, the Theory of Evolution and the Theory of Relativity cannot be expressed concisely enough to be considered a law. The biggest difference between a law and a theory is that a theory is much more complex and dynamic. A law describes a single action, whereas a theory explains an entire group of related phenomena. And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is the end result of that process.
Less broadly applicable statements are usually called principles (such as Pascal’s principle, which is applicable only in fluids), but the distinction between laws and principles often is not carefully made.
The models, theories, and laws we devise sometimes imply the existence of objects or phenomena as yet unobserved. These predictions are remarkable triumphs and tributes to the power of science. It is the underlying order in the universe that enables scientists to make such spectacular predictions. However, if experiment does not verify our predictions, then the theory or law is wrong, no matter how elegant or convenient it is. Laws can never be known with absolute certainty because it is impossible to perform every imaginable experiment in order to confirm a law in every possible scenario. Physicists operate under the assumption that all scientific laws and theories are valid until a counterexample is observed. If a good-quality, verifiable experiment contradicts a well-established law, then the law must be modified or overthrown completely.
The study of science in general and physics in particular is an adventure much like the exploration of uncharted ocean. Discoveries are made; models, theories, and laws are formulated; and the beauty of the physical universe is made more sublime for the insights gained.

### The Evolution of Natural Philosophy into Modern Physics

Physics was not always a separate and distinct discipline. It remains connected to other sciences to this day. The word physics comes from Greek, meaning nature. The study of nature came to be called “natural philosophy.” From ancient times through the Renaissance, natural philosophy encompassed many fields, including astronomy, biology, chemistry, physics, mathematics, and medicine. Over the last few centuries, the growth of knowledge has resulted in ever-increasing specialization and branching of natural philosophy into separate fields, with physics retaining the most basic facets. (See , , and .) Physics as it developed from the Renaissance to the end of the 19th century is called classical physics. It was transformed into modern physics by revolutionary discoveries made starting at the beginning of the 20th century.
Classical physics is not an exact description of the universe, but it is an excellent approximation under the following conditions: Matter must be moving at speeds less than about 1% of the speed of light, the objects dealt with must be large enough to be seen with a microscope, and only weak gravitational fields, such as the field generated by the Earth, can be involved. Because humans live under such circumstances, classical physics seems intuitively reasonable, while many aspects of modern physics seem bizarre. This is why models are so useful in modern physics—they let us conceptualize phenomena we do not ordinarily experience. We can relate to models in human terms and visualize what happens when objects move at high speeds or imagine what objects too small to observe with our senses might be like. For example, we can understand an atom’s properties because we can picture it in our minds, although we have never seen an atom with our eyes. New tools, of course, allow us to better picture phenomena we cannot see. In fact, new instrumentation has allowed us in recent years to actually “picture” the atom.
Some of the most spectacular advances in science have been made in modern physics. Many of the laws of classical physics have been modified or rejected, and revolutionary changes in technology, society, and our view of the universe have resulted. Like science fiction, modern physics is filled with fascinating objects beyond our normal experiences, but it has the advantage over science fiction of being very real. Why, then, is the majority of this text devoted to topics of classical physics? There are two main reasons: Classical physics gives an extremely accurate description of the universe under a wide range of everyday circumstances, and knowledge of classical physics is necessary to understand modern physics.
Modern physics itself consists of the two revolutionary theories, relativity and quantum mechanics. These theories deal with the very fast and the very small, respectively. Relativity must be used whenever an object is traveling at greater than about 1% of the speed of light or experiences a strong gravitational field such as that near the Sun. Quantum mechanics must be used for objects smaller than can be seen with a microscope. The combination of these two theories is relativistic quantum mechanics, and it describes the behavior of small objects traveling at high speeds or experiencing a strong gravitational field. Relativistic quantum mechanics is the best universally applicable theory we have. Because of its mathematical complexity, it is used only when necessary, and the other theories are used whenever they will produce sufficiently accurate results. We will find, however, that we can do a great deal of modern physics with the algebra and trigonometry used in this text.

### Summary

1. Science seeks to discover and describe the underlying order and simplicity in nature.
2. Physics is the most basic of the sciences, concerning itself with energy, matter, space and time, and their interactions.
3. Scientific laws and theories express the general truths of nature and the body of knowledge they encompass. These laws of nature are rules that all natural processes appear to follow.

### Conceptual Questions


# Introduction: The Nature of Science and Physics

## Physical Quantities and Units

### Learning Objectives

By the end of this section, you will be able to:
1. Perform unit conversions both in the SI and English units.

2. Explain the most common prefixes in the SI units and be able to write them in scientific notation.
The range of objects and phenomena studied in physics is immense. From the incredibly short lifetime of a nucleus to the age of the Earth, from the tiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the force between Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. To comprehend these vast ranges, we must also have accepted units in which to express them. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears—most physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.
We define a physical quantity either by  specifying how it is measured or by stating how it is calculated from other measurements. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of travel.
Measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way. (See .)
There are two major systems of units used in the world: SI units (also known as the metric system) and English units (also known as the customary or imperial system). English units were historically used in nations once ruled by the British Empire and are still widely used in the United States. Virtually every other country in the world now uses SI units as the standard; the metric system is also the standard system agreed upon by scientists and mathematicians. The acronym “SI” is derived from the French Système International.

### SI Units: Fundamental and Derived Units

 gives the fundamental SI units that are used throughout this textbook. This text uses non-SI units in a few applications where they are in very common use, such as the measurement of blood pressure in millimeters of mercury (mm Hg). Whenever non-SI units are discussed, they will be tied to SI units through conversions.
It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined only in terms of the procedure used to measure them. The units in which they are measured are thus called fundamental units. In this textbook, the fundamental physical quantities are taken to be length, mass, time, and electric current. (Note that electric current will not be introduced until much later in this text.) All other physical quantities, such as force and electric charge, can be expressed as algebraic combinations of length, mass, time, and current (for example, speed is length divided by time); these units are called derived units.

### Units of Time, Length, and Mass: The Second, Meter, and Kilogram

### The Second

The SI unit for time, the second (abbreviated s), has a long history. For many years it was defined as 1/86,400 of a mean solar day. More recently, a new standard was adopted to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth’s rotation). Cesium atoms can be made to vibrate in a very steady way, and these vibrations can be readily observed and counted. In 1967 the second was redefined as the time required for 9,192,631,770 of these vibrations. (See .) Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental units and can be no more accurate than are the fundamental units themselves.

### The Meter

The SI unit for length is the meter (abbreviated m); its definition has also changed over time to become more accurate and precise. The meter was first defined in 1791 as 1/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. By 1960, it had become possible to define the meter even more accurately in terms of the wavelength of light, so it was again redefined as 1,650,763.73 wavelengths of orange light emitted by krypton atoms. In 1983, the meter was given its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1/299,792,458 of a second. (See .) This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if the speed of light is someday measured with greater accuracy.

### The Kilogram

The SI unit for mass is the kilogram (abbreviated kg); it was previously defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the previously defined kilogram are also kept at the United States’ National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the world. The determination of all other masses could be ultimately traced to a comparison with the standard mass. Even though the platinum-iridium cylinder was resistant to corrosion, airborne contaminants were able to adhere to its surface, slightly changing its mass over time. In May 2019, the scientific community adopted a more stable definition of the kilogram. The kilogram is now defined in terms of the second, the meter, and Planck's constant, h (a quantum mechanical value that relates a photon's energy to its frequency).
Electric current and its accompanying unit, the ampere, will be introduced in Electric Current, Resistance, and Ohm's Law when electricity and magnetism are covered. The initial modules in this textbook are concerned with mechanics, fluids, heat, and waves. In these subjects all pertinent physical quantities can be expressed in terms of the fundamental units of length, mass, and time.

### Metric Prefixes

SI units are part of the metric system. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10.  gives metric prefixes and symbols used to denote various factors of 10.
Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple—there are 12 inches in a foot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.
The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of , and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of  are said to be of the same order of magnitude. For example, the number  can be written as , and the number  can be written as  Thus, the numbers  and  are of the same order of magnitude:  Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of  while the diameter of the Sun is on the order of

### Known Ranges of Length, Mass, and Time

The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times in . Examination of this table will give you some feeling for the range of possible topics and numerical values. (See  and .)

### Unit Conversion and Dimensional Analysis

It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.
Let us consider a simple example of how to convert units. Let us say that we want to convert 80 meters (m) to kilometers (km).
The first thing to do is to list the units that you have and the units that you want to convert to. In this case, we have units in meters and we want to convert to kilometers.
Next, we need to determine a conversion factor relating meters to kilometers. A conversion factor is a ratio expressing how many of one unit are equal to another unit. For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and so on. In this case, we know that there are 1,000 meters in 1 kilometer.
Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown:
Note that the unwanted m unit cancels, leaving only the desired km unit. You can use this method to convert between any types of unit.
Click Appendix C for a more complete list of conversion factors.

### Summary

1. Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements.
2. Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.
3. The four fundamental units we will use in this text are the meter (for length), the kilogram (for mass), the second (for time), and the ampere (for electric current). These units are part of the metric system, which uses powers of 10 to relate quantities over the vast ranges encountered in nature.
4. The four fundamental units are abbreviated as follows: meter, m; kilogram, kg; second, s; and ampere, A. The metric system also uses a standard set of prefixes to denote each order of magnitude greater than or lesser than the fundamental unit itself.
5. Unit conversions involve changing a value expressed in one type of unit to another type of unit. This is done by using conversion factors, which are ratios relating equal quantities of different units.

### Conceptual Questions

### Problems & Exercises


# Introduction: The Nature of Science and Physics

## Accuracy, Precision, and Significant Figures

### Learning Objectives

By the end of this section, you will be able to:
1. Determine the appropriate number of significant figures in both addition and subtraction, as well as multiplication and division calculations.

2. Calculate the percent uncertainty of a measurement.

### Accuracy and Precision of a Measurement

Science is based on observation and experiment—that is, on measurements. Accuracy is how close a measurement is to the correct value for that measurement. For example, let us say that you are measuring the length of standard computer paper. The packaging in which you purchased the paper states that it is 11.0 inches long. You measure the length of the paper three times and obtain the following measurements: 11.1 in., 11.2 in., and 10.9 in. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. In contrast, if you had obtained a measurement of 12 inches, your measurement would not be very accurate.
The precision of a measurement system refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). Consider the example of the paper measurements. The precision of the measurements refers to the spread of the measured values. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values. In that case, the lowest value was 10.9 in. and the highest value was 11.2 in. Thus, the measured values deviated from each other by at most 0.3 in. These measurements were relatively precise because they did not vary too much in value. However, if the measured values had been 10.9, 11.1, and 11.9, then the measurements would not be very precise because there would be significant variation from one measurement to another.
The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they are precise but not accurate. Let us consider an example of a GPS system that is attempting to locate the position of a restaurant in a city. Think of the restaurant location as existing at the center of a bull’s-eye target, and think of each GPS attempt to locate the restaurant as a black dot. In , you can see that the GPS measurements are spread out far apart from each other, but they are centered close to the actual location of the restaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in , the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, low accuracy measuring system.

### Accuracy, Precision, and Uncertainty

The degree of accuracy and precision of a measuring system are related to the uncertainty in the measurements. Uncertainty is a quantitative measure of how much your measured values deviate from a standard or expected value. If your measurements are not very accurate or precise, then the uncertainty of your values will be very high. In more general terms, uncertainty can be thought of as a disclaimer for your measured values. For example, if someone asked you to provide the mileage on your car, you might say that it is 45,000 miles, plus or minus 500 miles. The plus or minus amount is the uncertainty in your value. That is, you are indicating that the actual mileage of your car might be as low as 44,500 miles or as high as 45,500 miles, or anywhere in between. All measurements contain some amount of uncertainty. In our example of measuring the length of the paper, we might say that the length of the paper is 11 in., plus or minus 0.2 in. The uncertainty in a measurement, , is often denoted as  (“delta ”), so the measurement result would be recorded as

 . In our paper example, the length of the paper could be expressed as
The factors contributing to uncertainty in a measurement include:
1. Limitations of the measuring device,
2. The skill of the person making the measurement,
3. Irregularities in the object being measured,
4. Any other factors that affect the outcome (highly dependent on the situation).
In our example, such factors contributing to the uncertainty could be the following: the smallest division on the ruler is 0.1 in., the person using the ruler has bad eyesight, or one side of the paper is slightly longer than the other. At any rate, the uncertainty in a measurement must be based on a careful consideration of all the factors that might contribute and their possible effects.

### Percent Uncertainty

One method of expressing uncertainty is as a percent of the measured value. If a measurement  is expressed with uncertainty, , the percent uncertainty (%unc) is defined to be

### Uncertainties in Calculations

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division? If the measurements going into the calculation have small uncertainties (a few percent or less), then the method of adding percents can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation. For example, if a floor has a length of  and a width of , with uncertainties of  and , respectively, then the area of the floor is  and has an uncertainty of . (Expressed as an area this is , which we round to  since the area of the floor is given to a tenth of a square meter.)

### Precision of Measuring Tools and Significant Figures

An important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.01 millimeter. The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be.
When we express measured values, we can only list as many digits as we initially measured with our measuring tool. For example, if you use a standard ruler to measure the length of a stick, you may measure it to be . You could not express this value as  because your measuring tool was not precise enough to measure a hundredth of a centimeter. It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between  and , and they must estimate the value of the last digit. Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty. In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right. For example, the measured value  has three digits, or significant figures. Significant figures indicate the precision of a measuring tool that was used to measure a value.

### Zeros

Special consideration is given to zeros when counting significant figures. The zeros in 0.053 are not significant, because they are only placekeepers that locate the decimal point. There are two significant figures in 0.053. The zeros in 10.053 are not placekeepers but are significant—this number has five significant figures. The zeros in 1300 may or may not be significant depending on the style of writing numbers. They could mean the number is known to the last digit, or they could be placekeepers. So 1300 could have two, three, or four significant figures. (To avoid this ambiguity, write 1300 in scientific notation.) Zeros are significant except when they serve only as placekeepers.

### Significant Figures in Calculations

When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value. There are two different rules, one for multiplication and division and the other for addition and subtraction, as discussed below.
1. For multiplication and division: The result should have the same number of significant figures as the quantity having the least significant figures entering into the calculation. For example, the area of a circle can be calculated from its radius using . Let us see how many significant figures the area has if the radius has only two—say, . Then,
is what you would get using a calculator that has an eight-digit output. But because the radius has only two significant figures, it limits the calculated quantity to two significant figures or
even though  is good to at least eight digits.
2. For addition and subtraction: The answer can contain no more decimal places than the least precise measurement. Suppose that you buy 7.56-kg of potatoes in a grocery store as measured with a scale with precision 0.01 kg. Then you drop off 6.052-kg of potatoes at your laboratory as measured by a scale with precision 0.001 kg. Finally, you go home and add 13.7 kg of potatoes as measured by a bathroom scale with precision 0.1 kg. How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simple addition and subtraction:
Next, we identify the least precise measurement: 13.7 kg. This measurement is expressed to the 0.1 decimal place, so our final answer must also be expressed to the 0.1 decimal place. Thus, the answer is rounded to the tenths place, giving us 15.2 kg.

### Significant Figures in this Text

In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewer significant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for the situation posed. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Finally, if a number is exact, such as the two in the formula for the circumference of a circle, , it does not affect the number of significant figures in a calculation.

### Summary

1. Accuracy of a measured value refers to how close a measurement is to the correct value. The uncertainty in a measurement is an estimate of the amount by which the measurement result may differ from this value.
2. Precision of measured values refers to how close the agreement is between repeated measurements.
3. The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool.
4. Significant figures express the precision of a measuring tool.
5. When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.
6. When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.

### Conceptual Questions

### Problems & Exercises

Express your answers to problems in this section to the correct number of significant figures and proper units.


# Introduction: The Nature of Science and Physics

## Approximation

### Learning Objectives

By the end of this section, you will be able to:
1. Make reasonable approximations based on given data.
On many occasions, physicists, other scientists, and engineers need to make approximations or “guesstimates” for a particular quantity. What is the distance to a certain destination? What is the approximate density of a given item? About how large a current will there be in a circuit? Many approximate numbers are based on formulae in which the input quantities are known only to a limited accuracy. As you develop problem-solving skills (that can be applied to a variety of fields through a study of physics), you will also develop skills at approximating. You will develop these skills through thinking more quantitatively, and by being willing to take risks. As with any endeavor, experience helps, as well as familiarity with units. These approximations allow us to rule out certain scenarios or unrealistic numbers. Approximations also allow us to challenge others and guide us in our approaches to our scientific world. Let us do two examples to illustrate this concept.

### Summary

Scientists often approximate the values of quantities to perform calculations and analyze systems.

### Problems & Exercises


# Kinematics

## Introduction to One-Dimensional Kinematics

Objects are in motion everywhere we look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. And even in inanimate objects, there is continuous motion in the vibrations of atoms and molecules. Questions about motion are interesting in and of themselves: How long will it take for a space probe to get to Mars? Where will a football land if it is thrown at a certain angle? But an understanding of motion is also key to understanding other concepts in physics. An understanding of acceleration, for example, is crucial to the study of force.
Our formal study of physics begins with kinematics which is defined as the study of motion without considering its causes. The word “kinematics” comes from a Greek term meaning motion and is related to other English words such as “cinema” (movies) and “kinesiology” (the study of human motion). In one-dimensional kinematics and Two-Dimensional Kinematics we will study only the motion of a football, for example, without worrying about what forces cause or change its motion. Such considerations come in other chapters. In this chapter, we examine the simplest type of motion—namely, motion along a straight line, or one-dimensional motion. In Two-Dimensional Kinematics, we apply concepts developed here to study motion along curved paths (two- and three-dimensional motion); for example, that of a car rounding a curve.


# Kinematics

## Displacement

### Learning Objectives

By the end of this section, you will be able to:
1. Define position, displacement, distance, and distance traveled.
2. Explain the relationship between position and displacement.
3. Distinguish between displacement and distance traveled.
4. Calculate displacement and distance given initial position, final position, and the path between the two.

### Position

In order to describe the motion of an object, you must first be able to describe its position—where it is at any particular time. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board. (See .) In other cases, we use reference frames that are not stationary but are in motion relative to the Earth. To describe the position of a person in an airplane, for example, we use the airplane, not the Earth, as the reference frame. (See .)

### Displacement

If an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or a passenger moves toward the rear of an airplane), then the object’s position changes. This change in position is known as displacement. The word “displacement” implies that an object has moved, or has been displaced.
In this text the upper case Greek letter  (delta) always means “change in” whatever quantity follows it; thus,  means change in position. Always solve for displacement by subtracting initial position  from final position .
Note that the SI unit for displacement is the meter (m) (see Physical Quantities and Units), but sometimes kilometers, miles, feet, and other units of length are used. Keep in mind that when units other than the meter are used in a problem, you may need to convert them into meters to complete the calculation.

Note that displacement has a direction as well as a magnitude. The professor’s displacement is 2.0 m to the right, and the airline passenger’s displacement is 4.0 m toward the rear. In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction). The professor’s initial position is  and her final position is . Thus her displacement is
In this coordinate system, motion to the right is positive, whereas motion to the left is negative. Similarly, the airplane passenger’s initial position is  and his final position is , so his displacement is
His displacement is negative because his motion is toward the rear of the plane, or in the negative  direction in our coordinate system.

### Distance

Although displacement is described in terms of direction, distance is not. Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance has no direction and, thus, no sign. For example, the distance the professor walks is 2.0 m. The distance the airplane passenger walks is 4.0 m.

### Test Prep for AP Courses

### Section Summary

1. Kinematics is the study of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion.
2. Displacement is the change in position of an object.
3. In symbols, displacement  is defined to be

    where  is the initial position and  is the final position. In this text, the Greek letter  (delta) always means “change in” whatever quantity follows it. The SI unit for displacement is the meter (m). Displacement has a direction as well as a magnitude.
4. When you start a problem, assign which direction will be positive.
5. Distance is the magnitude of displacement between two positions.
6. Distance traveled is the total length of the path traveled between two positions.

### Conceptual Questions

### Problems & Exercises


# Kinematics

## Vectors, Scalars, and Coordinate Systems

### Learning Objectives

By the end of this section, you will be able to:
1. Define and distinguish between scalar and vector quantities.
2. Assign a coordinate system for a scenario involving one-dimensional motion.
What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector is any quantity with both magnitude and direction. Other examples of vectors include a velocity of 90 km/h east and a force of 500 newtons straight down.
The direction of a vector in one-dimensional motion is given simply by a plus

           or minus  sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector’s magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector.
Some physical quantities, like distance, either have no direction or none is specified. A scalar is any quantity that has a magnitude, but no direction. For example, a  temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km/h speed limit, a person’s 1.8 m height, and a distance of 2.0 m are all scalars—quantities with no specified direction. Note, however, that a scalar can be negative, such as a  temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows.

### Coordinate Systems for One-Dimensional Motion

In order to describe the direction of a vector quantity, you must designate a coordinate system within the reference frame. For one-dimensional motion, this is a simple coordinate system consisting of a one-dimensional coordinate line. In general, when describing horizontal motion, motion to the right is usually considered positive, and motion to the left is considered negative. With vertical motion, motion up is usually positive and motion down is negative. In some cases, however, as with the jet in , it can be more convenient to switch the positive and negative directions. For example, if you are analyzing the motion of falling objects, it can be useful to define downwards as the positive direction. If people in a race are running to the left, it is useful to define left as the positive direction. It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it.

### Test Prep for AP Courses

### Section Summary

1. A vector is any quantity that has magnitude and direction.
2. A scalar is any quantity that has magnitude but no direction.
3. Displacement and velocity are vectors, whereas distance and speed are scalars.
4. In one-dimensional motion, direction is specified by a plus or minus sign to signify left or right, up or down, and the like.

### Conceptual Questions


# Kinematics

## Time, Velocity, and Speed

### Learning Objectives

By the end of this section, you will be able to:
1. Explain the relationships between instantaneous velocity, average velocity, instantaneous speed, average speed, displacement, and time.
2. Calculate velocity and speed given initial position, initial time, final position, and final time.
3. Derive a graph of velocity vs. time given a graph of position vs. time.
4. Interpret a graph of velocity vs. time.
There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.

### Time

As discussed in Physical Quantities and Units, the most fundamental physical quantities are defined by how they are measured. This is the case with time. Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple—time is change, or the interval over which change occurs. It is impossible to know that time has passed unless something changes.
The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. We might, for example, observe that a certain pendulum makes one full swing every 0.75 s. We could then use the pendulum to measure time by counting its swings or, of course, by connecting the pendulum to a clock mechanism that registers time on a dial. This allows us to not only measure the amount of time, but also to determine a sequence of events.
How does time relate to motion? We are usually interested in elapsed time for a particular motion, such as how long it takes an airplane passenger to get from his seat to the back of the plane. To find elapsed time, we note the time at the beginning and end of the motion and subtract the two. For example, a lecture may start at 11:00 A.M. and end at 11:50 A.M., so that the elapsed time would be 50 min. Elapsed time  is the difference between the ending time and beginning time,
where  is the change in time or elapsed time,  is the time at the end of the motion, and  is the time at the beginning of the motion. (As usual, the delta symbol, , means the change in the quantity that follows it.)
Life is simpler if the beginning time  is taken to be zero, as when we use a stopwatch. If we were using a stopwatch, it would simply read zero at the start of the lecture and 50 min at the end. If , then .
In this text, for simplicity’s sake,
1. motion starts at time equal to zero
2. the symbol  is used for elapsed time unless otherwise specified

### Velocity

Your notion of velocity is probably the same as its scientific definition. You know that if you have a large displacement in a small amount of time you have a large velocity, and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.
Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use. Suppose, for example, an airplane passenger took 5 seconds to move −4 m (the negative sign indicates that displacement is toward the back of the plane). His average velocity would be
The minus sign indicates the average velocity is also toward the rear of the plane.
The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.
The smaller the time intervals considered in a motion, the more detailed the information. When we carry this process to its logical conclusion, we are left with an infinitesimally small interval. Over such an interval, the average velocity becomes the instantaneous velocity or the velocity at a specific instant. A car’s speedometer, for example, shows the magnitude (but not the direction) of the instantaneous velocity of the car. (Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity.) Instantaneous velocity  is the average velocity at a specific instant in time (or over an infinitesimally small time interval).
Mathematically, finding instantaneous velocity, , at a precise instant  can involve taking a limit, a calculus operation beyond the scope of this text. However, under many circumstances, we can find precise values for instantaneous velocity without calculus.

### Speed

In everyday language, most people use the terms “speed” and “velocity” interchangeably. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Thus speed is a scalar. Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed.
Instantaneous speed is the magnitude of instantaneous velocity. For example, suppose the airplane passenger at one instant had an instantaneous velocity of −3.0 m/s (the minus meaning toward the rear of the plane). At that same time his instantaneous speed was 3.0 m/s. Or suppose that at one time during a shopping trip your instantaneous velocity is 40 km/h due north. Your instantaneous speed at that instant would be 40 km/h—the same magnitude but without a direction. Average speed, however, is very different from average velocity. Average speed is the distance traveled divided by elapsed time.
We have noted that distance traveled can be greater than the magnitude of displacement. So average speed can be greater than average velocity, which is displacement divided by time. For example, if you drive to a store and return home in half an hour, and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, is zero for a round trip.) Thus average speed is not simply the magnitude of average velocity.
Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.-time graphs are displayed in . (Note that these graphs depict a very simplified model of the trip. We are assuming that speed is constant during the trip, which is unrealistic given that we’ll probably stop at the store. But for simplicity’s sake, we will model it with no stops or changes in speed. We are also assuming that the route between the store and the house is a perfectly straight line.)

### Test Prep for AP Courses

### Section Summary

1. Time is measured in terms of change, and its SI unit is the second (s). Elapsed time for an event is

where  is the final time and  is the initial time. The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just .
2. Average velocity  is defined as displacement divided by the travel time. In symbols, average velocity is

3. The SI unit for velocity is m/s.
4. Velocity is a vector and thus has a direction.
5. Instantaneous velocity  is the velocity at a specific instant or the average velocity for an infinitesimal interval.
6. Instantaneous speed is the magnitude of the instantaneous velocity.
7. Instantaneous speed is a scalar quantity, as it has no direction specified.
8. Average speed is the total distance traveled divided by the elapsed time. (Average speed is not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.

### Conceptual Questions

### Problems & Exercises


# Kinematics

## Acceleration

### Learning Objectives

By the end of this section, you will be able to:
1. Define and distinguish between instantaneous acceleration, average acceleration, and deceleration.
2. Calculate acceleration given initial time, initial velocity, final time, and final velocity.
In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration, the greater the change in velocity over a given time. The formal definition of acceleration is consistent with these notions, but more inclusive.
Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are , meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.
Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.
Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration.

### Instantaneous Acceleration

Instantaneous acceleration , or the acceleration at a specific instant in time, is obtained by the same process as discussed for instantaneous velocity in Time, Velocity, and Speed—that is, by considering an infinitesimally small interval of time. How do we find instantaneous acceleration using only algebra? The answer is that we choose an average acceleration that is representative of the motion.  shows graphs of instantaneous acceleration versus time for two very different motions. In (a), the acceleration varies slightly and the average over the entire interval is nearly the same as the instantaneous acceleration at any time. In this case, we should treat this motion as if it had a constant acceleration equal to the average (in this case about ). In (b), the acceleration varies drastically over time. In such situations it is best to consider smaller time intervals and choose an average acceleration for each. For example, we could consider motion over the time intervals from 0 to 1.0 s and from 1.0 to 3.0 s as separate motions with accelerations of  and , respectively.
The next several examples consider the motion of the subway train shown in . In (a) the shuttle moves to the right, and in (b) it moves to the left. The examples are designed to further illustrate aspects of motion and to illustrate some of the reasoning that goes into solving problems.
The graphs of position, velocity, and acceleration vs. time for the trains in  and  are displayed in . (We have taken the velocity to remain constant from 20 to 40 s, after which the train decelerates.)

### Sign and Direction

Perhaps the most important thing to note about these examples is the signs of the answers. In our chosen coordinate system, plus means the quantity is to the right and minus means it is to the left. This is easy to imagine for displacement and velocity. But it is a little less obvious for acceleration. Most people interpret negative acceleration as the slowing of an object. This was not the case in , where a positive acceleration slowed a negative velocity. The crucial distinction was that the acceleration was in the opposite direction from the velocity. In fact, a negative acceleration will increase a negative velocity. For example, the train moving to the left in  is sped up by an acceleration to the left. In that case, both  and  are negative. The plus and minus signs give the directions of the accelerations. If acceleration has the same sign as the velocity, the object is speeding up. If acceleration has the opposite sign as the velocity, the object is slowing down.

### Test Prep for AP Courses

### Section Summary

1. Acceleration is the rate at which velocity changes. In symbols, average acceleration  is

2. The SI unit for acceleration is .
3. Acceleration is a vector, and thus has a both a magnitude and direction.
4. Acceleration can be caused by either a change in the magnitude or the direction of the velocity.
5. Instantaneous acceleration  is the acceleration at a specific instant in time.
6. Deceleration is an acceleration with a direction opposite to that of the velocity.

### Conceptual Questions

### Problems & Exercises