The figure below represents a racetrack with semicircular sections connected by

Question

The figure below represents a racetrack with semicircular sections connected by straight sections. Each section has length d, and markers along the track are spaced d/4 apart. Two people drive cars counterclockwise around the track, as shown. Car X goes around the curves at constant speed v_c, increases speed at constant acceleration for half of each straight section to reach a maximum speed of 2v_c, then brakes at constant acceleration for the other half of each straight section to return to speed v_c. Car Y also goes around the curves at constant speed v_c, increases speed at constant acceleration for one-fourth of each straight section to reach the same maximum speed 2v_c, stays at that speed for half of each straight section, then brakes at constant acceleration for the remaining fourth of each straight section to return to speed v_c. On the figures below, draw an arrow showing the direction of the net force on each of the cars at the positions noted by the dots. If the net force is zero at any position, label the dot with 0. Indicate which car, if either, completes one trip around the track in less time, and justify your answer qualitatively without using equations.

Explanation / Answer

(b) Since both the cars have the same speed at the semi-circular section, both take the same amount of time to complete the curve. So the only difference arises when the car's are moving on the straight sections.

For car X it takes larger distance to reach the velocity of 2vc , which implies that the acceleration is slower(i.e it requires more time to reach the velocity of 2vc) and it takes same amount of time to deaccelerate to velocity vc in the other half of the straight section.

For car Y, the same velocity 2vc is achieved at a smaller distance, implying the acceleration is much faster for this car, and the deacceleration is also much faster, and also, covers half of straight section with a speed of 2vc. The acceleration of the car being higher, car Y completes the trip much faster.

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