usyed3/TransportBench huggingface dataset:
Problem: FTA represents Federal Transportation Administration, a federal government agency within the US Department of Transportation. True or False?
Solution: False (Federal Transit Administration)
Problem: In recent years, approximately 20\% of GDP is accounted for by expenses related to the transportation sector, and transportation covered nearly 10\% of household consumption expenditures. True or False?
Solution: nFalse (9.0\% of GDP in 2022; 16.8\% household consumption in 2022)
Problem: In Year 2000, the U.S. transportation industry shares more than 50\% of the nation’s energy consumption. True or False?
Solution: False (27.4\%.)
Problem: In year 2001, the U.S. transportation industry consumes more energy than the U.S. production industry. True or False?
Solution: False (Transportation: 27.3\%; Industrial: 33.7\% )
Problem: FHWA, FAA, AASHTO, IDOT, and AAR all stand for government transportation agencies. True or False?
Solution: False. The Association of American Railroads (AAR) is a (private) trade association.
Problem: In Year 2003, only about four thousand fatal transportation accidents in total occurred in the United States. True or False?
Solution: False (42,884 fatal motor vehicle fatalities)
Problem: Before the Interstate highway system was constructed, it took Lt. Col. Eisenhower’s convoy more than 60 days to travel from Washington DC to S.F in 1919. True or False.
Solution: True (62 days)
Problem: The transportation industry is highly deregulated, and government influence has become negligible. True or False? Explain your answer.
Solution: False. The transportation industry is governed by many federal and local authorities. In aviation, for example, the FAA tightly controls and monitors the US airspace. Other governmental agencies which oversee the industry through laws and policies include the FMCSA, NHTSA, EPA, STB, FMC, and the FTA. State and local DOTs also regulate and/or operate the industry.
Problem: Someone who never travels can benefit from the improvement of a transportation system. True or False? Explain your answer.
Solution: True. Improvement of transportation systems (e.g. by making them more efficient, resilient, and/or more sustainable) can benefit non-users by reducing cost/price of products and services. There are also indirect benefits to non-users from energy/environmental enhancements.
Problem: Public carriers are owned and operated by public agencies to provide transportation service to the society. True or False? Explain your answer.
Solution: False. Public carriers provide service to the general public. They can be owned by public agencies or private companies.
Problem: Public carriers (i.e., those serving the public), by definition, try to provide quality transportation service and maximize social welfare. True or False? Explain your answer.
Solution: False (public carriers include firms that are for-profit and are not necessarily concerned with maximizing social welfare)
Problem: Private carriers are generally owned and operated to serve own needs.  True or False? Explain your answer.
Solution: True. Private carriers are generally for-profit entities that are not obliged to serve the entire public. This is in contrast with public carriers who are obliged to serve the public.
Problem: Transportation systems generally include two components: moving parts (e.g., vehicles) and fixed parts (e.g., physical guideway and abstract network). True or False? Explain your answer.
Solution: False. They should also include operating rules and control mechanisms (e.g. right of way).
Problem: Railroad provides an energy-efficient and cheap mode for freight transportation. True or False?
Solution: True. Transporting freight by rail is often cheaper and much more energy efficient than by truck or air.
Problem: List five critical issues in transportation engineering.
Solution: Below are some issues:
\begin{enumerate}
    \item Improving efficiency (reducing congestion)
    \item Improving safety
    \item Responding to climate change
    \item Promoting equity and inclusion
    \item Building a strong economy
    \item Advancing public health
    \item Enhancing resiliency
    \item Workforce development
\end{enumerate}

\noindent Source: Critical Issues in Transportation for 2024 and Beyond (2024) and earlier versions.
Problem: List five transportation modes in transportation engineering.
Solution: \begin{enumerate}
    \item [a.] Railway transport
    \item [b.] Roadway transport
    \item [c.] Air transport
    \item [d.] Pipeline transport
    \item [e.] Maritime/waterway transport
\end{enumerate}
Problem: Briefly describe the components that constitute a typical transportation system, and give one example for each.
Solution: \begin{itemize}
    \item Moving parts. The parts of a transportation system that move people/goods, e.g. cars, trains, aircraft;
    \item  Physical infrastructure. The parts of a transportation system that act as guideways for the moving parts, e.g. roadway, railway, waterway;
    \item Control infrastructure. The parts of a transportation system that are put in place to manage or control the movement of the moving parts for reasons of safety, efficiency, e.g. right of way priorities.
\end{itemize}
Problem: Briefly describe how government is involved in the transportation industry (e.g., private and public carriers).
Solution: Below are some bullet points:
\begin{itemize}
    \item The government enacts laws and policies that control the physical usage of transportation infrastructure by the public, and public and private carriers
\item The government sets goals for the transportation industry (e.g. improve public health, mitigate environmental damage)
\item The government invests in planning, construction, and operations of transportation infrastructure
\item The government invests in transportation research and development

\end{itemize}
Problem: Briefly describe the possible positive and negative effects of two emerging technologies in the transportation industry.
Solution: Below are just two examples.
\begin{itemize}
    \item [1.] \textbf{Autonomous and connected vehicles} As autonomous and connected vehicle technology improves, the number of vehicle crashes will likely be reduced, and traffic flow efficiency can improve through the synchronization of connected autonomous vehicles. There may be further impacts on land use, urban form, and life style. However, autonomous vehicles might increase the risk of cyber-security, and disrupt the job security of drivers (e.g. taxi/truck/bus drivers).
    \item[2.] \textbf{Electric vehicles} Electric vehicles have the potential to significantly reduce carbon emissions from the transportation sector, and increase sustainability, but the batteries are resource-intensive and their extra weight can increase the amount of non-tailpipe emissions (e.g. brake dust). EV also impose higher charging time and driver anxiety.
\end{itemize}
Problem: Briefly summarize how improved transportation systems can benefit the society as a whole.
Solution: Society benefits from improved transportation systems because investing in well-planned and well-designed transportation systems improves the quality of life for its users by many metrics. From an economic standpoint, improving transportation systems can increase the time/space utility of goods, giving rise to specialization and economies of scale. In terms of health, improving transportation systems (e.g. by building more bike lanes and public transit) can decrease negative externalities such as air/noise pollution.
Problem: Describe the roles of the transportation “non-users” (i.e., government, professionals, and general public) in the U.S. transportation industry (regarding public and private carriers).
Solution: \textbf{Government}
on public carriers:
\begin{itemize}
    \item [a.] Own/operate vehicles and infrastructure
    \item[b.] Subsidize transit systems
    \item[c.] Regulate, e.g. controlling air pollution
    \item[d.] Expedite/facilitate transportation research through grants 
\end{itemize}

On private carriers:
\begin{itemize}
    \item [a.] Regulate private carriers; e.g., via licensing, axle load limits, safety regulations, and taxes.
\end{itemize}

\textbf{Professionals}
The primary goal of professionals in the transportation industry is to improve operations and efficiency through research, planning, policy-making, and educating the public. 

\textbf{Public} As "non-users", the public is still affected by the transportation industry through externalities such as noise/air pollution and taxation. The public also indirectly influences transportation policies.
Problem: Describe both positive and negative roles of transportation in the economy.
Solution: \textbf{Positive roles:} 

\begin{itemize}
    \item [a.] May improve time/space utility of goods. Note that time utility is the increase of the value of a good from reducing its transportation time (i.e. fast delivery of newspaper, no store sells one week old newspapers). The space utility is related to market expansion, urban sprawl etc. 
    \item [b.] Lead to changes in urban form, land use, e.g., by allowing people to work at jobs farther away. 
\end{itemize}

\textbf{Negative roles:} 
\begin{itemize}
    \item [a.] Consumes user time, money, and other public resources 
    \item [b.] The physical infrastructure and vehicles can be harmful to safety (via crashes) and the environment (via emissions).
\end{itemize}
Problem: Suppose that a metropolitan transit authority needs to provide transit service in a huge linear city of length $L$. The city is homogeneous everywhere. The daily cost of providing transit service in this area is $c_1 x^{-1/2} + c_2 x^2$ (\$/day per station), where $x \ll L$ is the length of the catchment area served by one station along the line and constants $c_1, c_2 > 0$. Determine $n^*$, the optimal number of transit stations, that minimizes total cost incurred to the authority per day. Express it in terms of $L$, $c_1$, $c_2$.
Solution: Since there are $n = L/x$ bus stops in the transit system, each with cost $c_1x^{-\frac{1}{2}} + c_2x^2$, we must minimize the function

\[
\min \frac{L}{x}\left( c_1 x^{-\frac{1}{2}} + c_2 x^2 \right)
\]

\[
 = \min L\left( c_1 x^{-\frac{3}{2}} + c_2 x \right)
\]

Minimizing the function by taking the derivative, setting it to 0, and solving for $x$, we have
\[
x^* = \left( \frac{9c_1^2}{4c_2^2} \right)^{\frac{1}{5}}
\]

\[
n^* = L \left( \frac{4c_2^2}{9c_1^2}\right)^\frac{1}{5}
\]
Problem: Upon successfully running the “widget” plant at Pittsburgh, you are promoted to manage a newly established overseas manufacturing plant at Arica, the most northern city in Chile. Chile can be considered a linear country that is 2500 miles in length. Your plant produces the widgets at $C = 8.00$ per unit. A public carrier is hired to deliver the widgets to the customers at a cost rate of $f = 10^{-3}$ dollars per widget-mile. Population of potential customers is uniformly distributed with a density of $\delta = 5$ people/mi. Every customer will need to buy $D = 2$ widgets per person per year if the price is no more than $10$ per widget.

\begin{itemize}
    \item [a.] What are your plant’s total revenue, total cost, and total profit?
    \item [b.] Due to local government’s policy, for any widget sold to the southern part of the country (beyond 1500 miles of length), you are now charged with a local tax of \$0.50. Nothing else changes. What will be your total revenue, cost, and profit?

\end{itemize}
Solution: \begin{itemize}
    \item [a.] First, assume there is no competitor. The revenue, \(R\), will be

\[
R = L\delta PD
\]

where \(L\) is the distance to the end point of the serviced length. The total cost will be the sum of the transportation cost, \(T\), and manufacturing cost, \(Z\):

\[
Z = L\delta CD
\]

\[
T = f \delta D \int_0^L x \, dx
\]

\[
T = fD \delta \frac{L^2}{2}
\]

The profit for a given \(L\) can then be found by the equation:

\[
\text{Profit} = R - Z - T
\]

\[
\text{Profit} = L\delta PD - L\delta CD - f\delta D \frac{L^2}{2}
\]

We can maximize the profit by taking the derivative, setting it to 0, and solving for \(L\):

\[
L^* = \frac{P - C}{f}
\]

which yields a service length of 2000 miles.

The revenue is then \$200,000.00, the total cost is \$180,000.00, and the profit is \$20,000.00.


    \item [b.] This tax will apply to 1000 miles of our current service. For a given \(L\), our new revenue is still 

\[
R = L\delta PD
\]

But our cost is now the sum of the manufacturing cost, \(Z\), the tax, \(F\), and the transportation cost, \(T\):

\[
Z = L\delta CD
\]

\[
T = f\delta D \int_0^L x \, dx
\]

\[
T = f\delta D \frac{L^2}{2}
\]

\[
F = 0.5 (L - 1000)\delta D
\]

Again, taking the derivative of the profit equation, setting it to 0, and solving for \(L\) gives the equation for \(L^*\):

\[
L^* = \frac{P - C - 0.5}{f}
\]

which gives a service length of 1500 miles. Therefore, our revenue is 

\[
R = 1500\delta PD = \$150,000.0
\]

Our cost is 

\[
Z + T + F = 1500\delta CD + f\delta D \frac{1500^2}{2} + 0.5 (1500 - 1000)\delta D = \$133,750.0
\]

So our profit is then \$16,250.0.

\end{itemize}
Problem: Suppose that you have one widget plant at the center of a sufficiently large country of size $S$ mi$^2$, where population is uniformly distributed with a density of $\delta$ people/mi$^2$. The distances are measured along straight lines (Euclidean metric). The production cost of widgets is $C$ dollars per unit, and the selling price is $P$ per unit, and knows that it can sell $D$ widgets per person per year everywhere in the country. Transportation costs include a fixed portion of $F$ per unit and a variable cost of $f$ dollars per widget-mile. Suppose $P > C + F$.

\begin{enumerate}
    \item[a.] Determine the shape and size of your market (the area your plant will serve). 
    \item[b.] What will be the profit of this one widget plant when $f = 0$?
\end{enumerate}
Solution: \begin{itemize}
    \item [a.] The shape of the market will be circular since it is a Euclidean metric. 
    The boundary of the market will be at the point where the revenue from selling one widget is equal to the cost of producing and transporting it, i.e. $P = C + F + fr$ where $r$ is the radius. Therefore, $r = (P – C – F)/f$. 
    \item[b.] If there is no variable transportation cost, then it will be profitable to serve the entire country under a fixed cost. So the total annual profit is  $M= (P-C-F) \delta S D$. 
\end{itemize}
Problem: Decision sight distance is introduced to engineering practice because stopping sight distance may preclude drivers from performing evasive maneuvers. True or False? Explain your answer.
Solution: True. There are situations where drivers have to use a longer reaction/decision time (than what is normally used in computing stopping sight distance) to determine (and conduct) complex evasive maneuvers.
Problem: Generally, stopping sight distance (the distance necessary for the vehicle to come to a full stop) is longer than the decision sight distance. True or False? Explain your answer.
Solution: False. Stopping sight distance is the minimum distance required to perceive-interpret-react and brake to a full stop. Decision sight distance is longer because it is the distance the driver needs to perceive and react to more complex situations. In these cases, the driver must digest navigational or hazard information and select an appropriate response (which may not be just braking), the distance traveled is larger than the stopping sight distance.
Problem: Briefly state the definition/components of perception-reaction time, their normal design values.
Solution: Reaction to a stimulus is usually divided into three stages 
\begin{itemize}
    \item \textit{Perception}: \, negligible if a person is warned; about 1 sec if not warned, or 0 sec if the driver is fully alerted. 
    \item  \textit{Interpretation}: \,  depends on complexity; e.g. ~ 1 sec for 3 words 
    \item  \textit{Decision/Reaction}: \, ~ 0.6 – 1.5 sec (use high end for design to be on the safe side).
\end{itemize}
Problem: Suppose a student uses a falling ruler to measure reaction time. He noticed a significant difference across trials (i.e., sometimes the ruler fell to the ground, while some other times it did not). What can we infer from that observation?
Solution: The reaction time of the student has high variance, possibly because the subject of the test may or may not be fully focused.
Problem: Suppose a student uses a falling ruler to measure reaction time. Before the ruler is released, the 0-inch mark is at the same height of the student’s hand. Suppose a student is able to grab the falling ruler at the 10-inch mark. Ignore air resistance. What is the student’s reaction time?
Solution: First, convert 10 inches to feet $\rightarrow$ 0.83 ft. Using the kinematic equation:

\[
x = x_0 + v_0 t + \frac{1}{2}at^2,
\]

where \(x_0=0, v_0=0, a = 32.2 \, \text{ft/s}^2\). We see that the reaction time was 0.228 seconds.
Problem: Suppose a student uses a falling ruler to measure reaction time. Assume the length of the ruler is 10 inch. Before the ruler is released, the 0-inch mark is at the same height of the student’s hand. Suppose a student is not able to grab the falling ruler. Ignore air resistance. What is the minimum value of the student’s reaction time?
Solution: First, convert 10 inches to feet $\rightarrow$ 0.83 ft. Using the kinematic equation:

\[
x = x_0 + v_0 t + \frac{1}{2}at^2 > 0.83 \text{ ft},
\]

where \(x_0=0, v_0=0, a = 32.2 \, \text{ft/s}^2\). We see that the reaction time $t >0.228$ seconds.
Problem: Due to grade resistance (from gravity), a vehicle will have a higher fuel consumption rate (e.g., per mile) when its tires are flat. True or False? Explain your answer.
Solution: False (A vehicle will have a higher fuel consumption rate with flat tires, but due to increased rolling resistance; grade resistance will remain the same)
Problem: The rolling resistance force (on moving vehicles) is related to the slope/grade of the road. True or False? Explain your answer.
Solution: False (rolling resistance is primarily due to uneven deformation of the tire and ground surface while the tire rolls on the ground)
Problem: In steady-state (stationary) traffic, density = flow $\times$ speed. True or False? Explain your answer.
Solution: False. flow = density $\times$ (space-mean speed)
Problem: At a signalized intersection, everything else being the same, the presence of a downhill grade will increase the likelihood for a driver to be in a dilemma zone. True or False? Explain your answer.
Solution: True (Downhill grade increases minimum stopping distances, which tends to widen the dilemma zone.)
Problem: If the speed of a vehicle keeps increasing, the aerodynamic resistance will eventually exceed the rolling resistance, because the aerodynamic resistance depends on the velocity of the vehicle while the rolling resistance does not. True or False? Explain your answer.
Solution: False (rolling resistance increases with speed; e.g., when speed is zero, there is no rolling resistance.)
Problem: The magnitude of aerodynamic resistance force (on moving vehicles) is directly proportional to the vehicle weight, air density, and vehicle speed. True or False? Explain your answer.
Solution: False (not directly related to vehicle weight, and proportional to the square of vehicle speed; also dependent on the frontal cross-sectional area size)
Problem: Aerodynamic resistance is typically the most important factor affecting train resistance at train speeds below 40 mph. True or False? Explain your answer.
Solution: False: The aerodynamic resistance of a train is normally not the most prominent at speeds below 40 mph. Aerodynamic resistance increases with the square of speed, so it becomes the most important factor at higher speeds (e.g., > 65 mph).
Problem: Describe basic resistance forces of vehicles, and for each resistance force, list one or more factors that influence its value.
Solution: \begin{itemize}
    \item[a.] Rolling resistance
    \begin{itemize}
        \item[i.] Weight or mass
        \item[ii.] Road surface rigidity
        \item[iii.] Tire rigidity/inflation
        \item[iv.] Speed
    \end{itemize}
    \item[b.] Aerodynamic resistance (drag)
    \begin{itemize}
        \item[i.] Speed
        \item[ii.] Air density
        \item[iii.] Frontal cross-sectional area size
        \item[iv.] Shape/size of vehicle (due to turbulence)
    \end{itemize}
    \item[c.] Grade resistance (gravity)
    \begin{itemize}
        \item[i.] Weight or mass
        \item[ii.] Grade of road
    \end{itemize}
\end{itemize}
Problem: At time \( t_0 \), a vehicle is with velocity \( v_0 \) at location \( x_0 \). Derive the location profile of a vehicle, \( x(t) \), for \( t \ge t_0 \), when acceleration is constant; i.e., \( a(x, v, t) \equiv a \). Show intermediate steps.
Solution: The location profile will depend on the initial velocity, initial position, and acceleration constant. To understand how the position will change due to acceleration, it is helpful to plot velocity versus time which we can do because the acceleration is constant.
\begin{figure}[h!]
    \centering
    \includegraphics[width=0.5\linewidth]{img/P4_9.png}
\end{figure}
 
The equation for this line is simply \( v\left(t\right)=v_0+a\left(t-t_0\right) \). Because position is the integral of velocity, we can obtain the location profile by integrating this equation with respect to time
\[
x\left(t\right)=x_0+v_0(t-t_0)+a\left(t-t_0\right)^2/2
\]
Problem: A motorcycle’s skid mark at an accident site is 70 feet long. Collision (onto a parked work-zone construction vehicle) occurred at 20 mile/hour. The road is level. The friction coefficient is 0.35. Help the police to determine the motorcycle’s speed when its brakes were first applied. Ignore air resistance.
Solution: First, convert 20 mph to $29.33$ ft/s. We can use the kinematic equation below to find the initial speed:

\[\
u^2 = u_0^2 + 2a\Delta x.
\]

Noting that the deceleration due to braking is $fg$ , we have  
\[
u_0 = \sqrt{u^2 + 2fg \Delta x},
\]

where \(g = 32.2 \, \text{ft/s}^2\), \(f = 0.35\), \(u = 29.33 \, \text{ft/s}\), and \(x = 70 \, \text{ft}\). Solving for \(u_0\), we have that the initial speed is 49.38 ft/s or 33.66 mph.
Problem: A motorcycle’s skid mark at an accident site is 80 feet long. Impact occurred at 20 mile/hour. The road is level. The friction coefficient is 0.3. Determine the motorcycle speed when its brakes were first applied. Ignore air resistance.
Solution: First, convert 20 mph to $ 29.33$ ft/s. We can use the kinematic equation below to find the initial speed:

\[\
u^2 = u_0^2 + 2a\Delta x.
\]

Noting that the deceleration due to braking is $fg$ , we have  
\[
u_0 = \sqrt{u^2 + 2fg \Delta x},
\]

where \(g = 32.2 \, \text{ft/s}^2\), \(f = 0.3\), \(u = 29.33 \, \text{ft/s}\), and \(x = 80 \, \text{ft}\). Solving for \(u_0\), we have that the initial speed is 49.05 ft/s or 33.44 mph.
Problem: In horizontal curve design, for a given design speed, the larger the road radius, the larger the rate of super-elevation. True or False? Explain your answer.
Solution: False. A larger road radius will decrease the centrifugal force experienced by a vehicle as compared to a smaller radius with the same design speed, thus reducing the required super-elevation.
Problem: While designing an equal-tangent vertical curve, given initial and final roadway grades and PVI, the parameters in the parabolic function can normally be determined once we find the curve length. True or False? Explain your answer.
Solution: True. The equation for an equal-tangent vertical curve is
\[
y = \frac{g_2-g_1}{L}x^2 + g_1x + e_{PVC},
\]
where $g_1$ and $g_2$ are the grades expressed as a decimal,
$L$ is the curve length, and $e_{PVC}$ is the elevation of the PVC. The value of $e_{PVC}$ can be easily found from the elevation of the PVI, as PVC is $L/2$ upstream of the PVI (at $g_1$ grade).
Problem: In horizontal curve design, for a given design speed, the larger the road radius, the smaller the rate of super-elevation. True or False? Explain your answer.
Solution: True. A larger road radius will decrease the centrifugal force experienced by a vehicle as compared to a smaller radius with the same design speed, thus reducing the required super-elevation.