Question

Whipple is confused about the connection between the velocity and acceleration of the tennis ball. he decides to compare the velocity of the ball and the acceleration of the ball at the apex of the ball's motion while varying the speed of the elevator. he runs the experiment for a wide range of positive speeds of the elevator and records the speed and acceleration of the ball at the top of its motion. what can whipple conclude from these data? the speed of the ball is always positive and the acceleration is always equal to −g at the instant the ball reaches the top of its motion. the speed of the ball and the acceleration are both zero when the ball reaches the top of its motion. the speed of the ball is always zero and the acceleration is always −g at the instant the ball reaches the top of its motion. the speed of the ball is always negative and the acceleration is always equal to −g at the instant the ball reaches the top of its motion.

Answer 1

The speed of the ball is always zero and the acceleration is always -g when it reaches the top of its motion. This is because when the ball is free, only gravity acts on it which is always downwards, hence g is the net acceleration and it is always negative. However the velocity does not direction change instantly, negative acceleration first slows down the ball with a positive velocity, until that point the ball keeps moving up, then the ball velocity becomes zero just before changing direction and becoming negative after which the ball will now go down along gravity. Hence the ball velocity is zero at the top (neither going up nor down). Mathematically this can be seen as velocity is the integration of acceleration.