In introductory kinematics, which quantity is defined as the rate at which velocity changes over time?

• A. Displacement
• B. Velocity
• C. Jerk
• D. Acceleration

Answer: (D)

Verified step by step guidance

1. Understand the definitions of the given quantities: Displacement is the change in position, Velocity is the rate of change of displacement, and Acceleration is the rate of change of velocity over time.
2. Recall that acceleration is mathematically defined as the derivative of velocity with respect to time, expressed as \(\\mathbf{a} = \\frac{d\\mathbf{v}}{dt}\).
3. Recognize that jerk is the rate of change of acceleration, which is a higher-order derivative and not the quantity asked for in this problem.
4. Conclude that since the problem asks for the rate at which velocity changes over time, the correct quantity is acceleration.
5. Summarize that acceleration measures how quickly velocity changes, making it the correct answer among the options provided.