The derivative of velocity with respect to time is which function?

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

Answer: (B)

Acceleration. The rate at which velocity changes with time is what acceleration measures. If velocity is v(t), then acceleration is a(t) = dv/dt. Since velocity is itself the rate of change of position (v = dx/dt), acceleration is the second derivative of position (a = d^2x/dt^2). This captures changes in speed and/or direction. If velocity is constant, dv/dt = 0, so acceleration is zero. Jerk would be the derivative of acceleration, not of velocity.