Starting from rest, a car accelerates down a straight road with constant acceleration a for a time t, then the direction of the acceleration is reversed, i.e., it is -a, and the car comes to a stop in an additional time t, the time for the whole trip being 2t. At what time, or times, is the average velocity of the car for the trip equal to its instantaneous velocity during the trip?
A) There is no such time.
B) It is at the halfway point at t.
C) This occurs at 2 times, at 0.5 t and 1.5 t.
D) This occurs at 2 times, at 0.707 t and 1.293 t.

Question

Quizplus · Accepted Answer

The average velocity is the total displacement divided by the total time. Since the car returns to its starting point, the total displacement is zero, making the average velocity zero. The instantaneous velocity is zero at 0.5t (when the car reaches its maximum speed) and at 1.5t (when the car comes to a stop).

Starting from Rest, a Car Accelerates Down a Straight Road