Final answer:
The acceleration of a bouncing ball is directed towards the change in velocity, which causes the ball to decelerate when moving against gravity and accelerate when moving with gravity.
Step-by-step explanation:
The relationship between acceleration and the motion of a bouncing ball can be understood by analyzing the direction of the ball's acceleration with respect to its velocity. When a ball is thrown upwards, it slows down due to gravity pulling it downwards, indicating deceleration. Similarly, as the ball falls back to the ground, gravity causes it to accelerate in the direction of its motion.
In more complex scenarios, such as a ball that also has a horizontal component of velocity (for example if it is thrown forward), Newton's Second Law of Motion indicates that the ball will continue to move with the same horizontal momentum unless acted on by an external force. This is due to the horizontal motion being independent of vertical acceleration. When the ball bounces off a wall or changes direction, the acceleration is in the direction of the change in velocity.
In a uniform circular motion, for instance, the direction of acceleration is towards the center of the circle, even if the magnitude of velocity is constant. This is because acceleration is not only the change in speed but also in direction. Thus, the bouncing ball's motion is a vivid demonstration of how acceleration can influence an object's trajectory and velocity in various ways.