Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:
A) it is passing car A.
B) it has the same linear (tangential) acceleration as car A.
C) it has the same centripetal acceleration as car A.
D) it has the same total acceleration as car A.
E) it has traveled farther than car A since starting.

Question

Quizplus · Accepted Answer

When both cars have the same tangential velocity, they are traveling at the same speed, but in different positions along the circular track. Since they are traveling at the same speed, they have the same tangential acceleration. However, their centripetal accelerations are determined by their positions on the track, which are different. Therefore, car B does not necessarily have the same centripetal acceleration as car A until it reaches the same position on the track. However, once it reaches that position, it will have the same centripetal acceleration as car A, since both are traveling at the same speed and radius. The other choices are incorrect because there is no information provided about passing or total distance traveled, and the tangential acceleration is already stated to be constant for car B.

Two Cars Are Traveling Around Identical Circular Racetracks