Which graph best represents the velocity–time graph for a ball that is dropped from rest and bounces repeatedly? A B C D - AQA - A-Level Physics - Question 23 - 2017 - Paper 1

To determine the correct velocity–time graph for a ball that is dropped from rest and bounces repeatedly, we must understand the behavior of the ball during its motion:

1. Initial Drop: When the ball is first dropped, it accelerates downwards due to gravity, leading to an increase in velocity.
2. First Bounce: Upon hitting the ground, the ball's velocity rapidly changes direction (becomes positive) as it bounces back upwards, although it will have a lower peak velocity than the drop due to energy loss (i.e., not reaching the original height).
3. Subsequent Bounces: Each subsequent bounce will follow a similar pattern but with decreasing heights and velocities, creating a series of triangular shapes on the graph.

With these points in mind, we analyze the given options:

• Graph A shows oscillating motion but the pattern is too smooth and not representative of repeated bounces.
• Graph B represents a similar oscillatory behavior but with alternating slopes that indicate an increase followed by a drop, which does not align with the mechanics of bounces.
• Graph C shows sharp changes in velocity, which is not consistent with the continuous nature of free-fall and bouncing.
• Graph D shows the correct pattern of increasing and decreasing velocity with each bounce, illustrating the energy lost with each successive impact.

Thus, the correct answer is D, as it best represents the velocity–time relationship of a ball dropped from rest and bouncing repeatedly.