Final answer:
Velocity cannot be constant if acceleration is not zero, because acceleration implies a change in velocity. An example is uniform circular motion, where the speed is constant but direction changes, causing acceleration. When a ball is thrown upwards, the velocity is zero at the peak but acceleration due to gravity is not.
Step-by-step explanation:
It is not possible for velocity to be constant while acceleration is not zero. Velocity is a vector quantity that includes both speed and direction. Therefore, if an object's velocity is constant, this means that both its speed and direction of motion is unchanging. However, acceleration is defined as the rate of change of velocity. If acceleration is not zero, it implies that there is a change in velocity, either in magnitude or direction or both.
An example where velocity is constant while acceleration is not zero is uniform circular motion. In such motion, the speed of the object may remain constant, but the direction of the velocity changes continuously as the object follows a circular path. This change in direction is an acceleration towards the center of the circle, known as centripetal acceleration.
As for a scenario where velocity is zero yet acceleration is not zero, consider a ball thrown vertically upwards. At the peak of its trajectory, the ball's velocity is zero, but it experiences a non-zero acceleration due to gravity, which is directed downwards.