Question: A ball thrown vertically upward rises to a maximum height and then falls to the ground. What are the ball's velocity and acceleration at the instant it reaches its maximum height?
Answer: When the ball is released it has an initial upward velocity. It also has a constant downward acceleration due to gravity. As it moves up its (upward) velocity steadily decreases because of the downward acceleration until at one instant the velocity is zero. Afterward the velocity becomes increasingly negative (that is, directed downward) and the ball moves down. At the instant the velocity becomes zero the ball has reached its maximum height; thereafter it falls back toward the ground. Thus at the maximum height the ball has zero velocity and a downward acceleration of gravity g.