Which of the following scenarios involves $a$cceleration?

• A. A ball resting on the ground
• B. A car moving at a constant $v$ in a straight line
• C. A runner maintaining a steady $v$ around a circular track
• D. A cyclist slowing down as they approach a stop sign

Answer: (D)

Verified step by step guidance

1. Recall the definition of acceleration: acceleration is the rate of change of velocity with respect to time. This means acceleration occurs if there is any change in the speed or direction of an object's motion.
2. Analyze each scenario: - A ball resting on the ground has zero velocity and no change in velocity, so acceleration is zero. - A car moving at a constant velocity in a straight line has no change in speed or direction, so acceleration is zero. - A runner maintaining a steady velocity around a circular track has constant speed but changing direction, so there is acceleration due to the change in direction (centripetal acceleration). - A cyclist slowing down as they approach a stop sign is changing speed, so there is acceleration (specifically, deceleration).
3. Understand that acceleration can be caused by changes in speed (magnitude of velocity) or changes in direction (even if speed is constant).
4. Identify that the correct answer involves a change in speed, which is the cyclist slowing down, indicating acceleration.
5. Summarize that acceleration is present whenever velocity changes, either in magnitude or direction, and the cyclist slowing down is a clear example of acceleration.