Car drag racing takes place over a distance of a mile 402 m) from a standing start. If a car mass 1500 kg) could be propelled forward with a pulling force equal to that of gravity, what would be the change in kinetic energy and the terminal speed of the car in mph) at the end of the race? For comparison, a modern, high-performance sports car may reach a terminal speed of just over 100 mph = 44.7 m/s.)

Question

Car drag racing takes place over a distance of a  mile 402 m) from a standing start. If a car mass 1500 kg) could be propelled forward with a pulling force equal to that of gravity, what would be the change in kinetic energy and the terminal speed of the car in mph) at the end of the race? For comparison, a modern, high-performance sports car may reach a terminal speed of just over 100 mph = 44.7 m/s.)

Quizplus · Accepted Answer

First, we need to calculate the work done by the pulling force on the car. Let's assume the pulling force is constant throughout the race. The work done is given by:

work = force x distance = (mass x acceleration) x distance

Since the pulling force is equal to the weight of the car (mg), we can write:

work = mg x distance = 1500 kg x 9.81 m/s^2 x 402 m = 5.92 MJ

This is the total work done on the car during the race. This work is converted into kinetic energy at the end of the race, when the drag force and the pulling force balance each other out and the car reaches its terminal velocity. We can use the work-energy theorem to find the change in kinetic energy:

work = change in kinetic energy = (1/2) x mass x (terminal velocity)^2

Solving for the terminal velocity, we get:

terminal velocity = sqrt(2 x work / mass) = sqrt(2 x 5.92 MJ / 1500 kg) = 88.8 m/s

Converting to mph, we get:

terminal velocity = 88.8 m/s x 2.237 = 198.5 mph

Since this is higher than the maximum terminal velocity of a high-performance sports car, we know that our assumption of a constant pulling force is not realistic. However, the question only asks for the final velocity and not for the details of the motion during the race, so we can still choose answer E as the best option based on the calculations above.

Car Drag Racing Takes Place Over a Distance of a