Context: Speed is an important aspect of motion. It is a measure of how fast or slow something moves. It depends on how far something travels and how long it takes to travel that far. Speed can be calculated using this general formula: speed = distance time A familiar example is the speed of a car. In the U.S., this is usually expressed in miles per hour (see Figure 12.6). If your family makes a car trip that covers 120 miles and takes 3 hours, then the cars speed is: speed = 120 mi = 40 mi/h 3h The speed of a car may also be expressed in kilometers per hour (km/h). The SI unit for speed is meters per second (m/s). When you travel by car, you usually dont move at a constant speed. Instead you go faster or slower depending on speed limits, traffic, traffic lights, and many other factors. For example, you might travel 65 miles per hour on a highway but only 20 miles per hour on a city street (see Figure 12.7). You might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars. The speed of a moving car or other object at a given instant is called its instantaneous speed. It may vary from moment to moment, so it is hard to calculate. Its easier to calculate the average speed of a moving object than the instantaneous speed. The average speed is the total distance traveled divided by the total time it took to travel that distance. To calculate the average speed, you can use the general formula for speed that was given above. Suppose, for example, that you took a 75-mile car trip with your family. Your instantaneous speed would vary throughout the trip. If the trip took a total of 1.5 hours, your average speed for the trip would be: average speed = 75 mi = 50 mi/h 1.5 h You can see a video about instantaneous and average speed and how to calculate them at this URL: MEDIA Click image to the left or use the URL below. URL: You Try It! Problem: Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri 15 minutes to make the round trip. What was her average speed for the entire trip? The motion of an object can be represented by a distance-time graph like the one in Figure 12.8. A distance-time graph shows how the distance from the starting point changes over time. The graph in Figure 12.8 represents a bike trip. The trip began at 7:30 AM (A) and ended at 12:30 PM (F). The rider traveled from the starting point to a destination and then returned to the starting point again. In a distance-time graph, the speed of the object is represented by the slope, or steepness, of the graph line. If the line is straight, like the line between A and B in Figure 12.8, then the speed is constant. The average speed can be calculated from the graph. The change in distance (represented by Dd) divided by the change in time (represented by Dt): speed = Dd Dt For example, the speed between A and B in Figure 12.8 is: speed = Dd 20 km 0 km 20 km = = = 20 km/h Dt 8:30 7:30 h 1h If the graph line is horizontal, as it is between B and C, then the slope and the speed are zero: speed = Dd 20 km 20 km 0 km = = = 0 km/h Dt 9:00 8:30 h 0.5 h You Try It! Problem: In Figure 12.8, calculate the speed of the rider between C and D. If you know the speed of a moving object, you can also calculate the distance it will travel in a given amount of time. To do so, you would use this version of the general speed formula: 
 Question: steepness of a graph line
Output: slope