Which of the following is an example of acceleration?

• A. A car increases its speed from $20$ km/h to $40$ km/h in $5$ seconds.
• B. A train remains stationary at a platform.
• C. A runner jogs around a circular track at a constant speed.
• D. A cyclist moves at a constant speed of $15$ km/h in a straight line.

Answer: (A)

Verified step by step guidance

1. Understand that acceleration is defined as the rate of change of velocity with respect to time. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction.
2. Identify that acceleration occurs when there is a change in the speed or direction of an object. This means acceleration can happen if an object speeds up, slows down, or changes direction.
3. Analyze each option: - A car increasing its speed from 20 km/h to 40 km/h means its velocity magnitude is changing, so it is accelerating. - A train remaining stationary means no change in velocity, so no acceleration. - A runner jogging around a circular track at constant speed changes direction continuously, so there is acceleration due to change in velocity direction. - A cyclist moving at constant speed in a straight line has no change in speed or direction, so no acceleration.
4. Recognize that the problem asks for an example of acceleration, so any scenario where velocity changes (in magnitude or direction) qualifies.
5. Conclude that the car increasing its speed is a clear example of acceleration because its speed (magnitude of velocity) changes over time.