The second derivative of the position function is the which function?

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

Answer: (B)

When you think of position x(t) as a function of time, its first derivative dx/dt gives velocity—the rate at which position changes. The second derivative, d^2x/dt^2, describes how that velocity is changing over time, which is acceleration. So a(t) = d^2x/dt^2 is acceleration. For a quick check, if x(t) = t^3, then v = 3t^2 and a = 6t, showing the second derivative indeed yields acceleration. Jerk is the third derivative, d^3x/dt^3, and displacement is simply the position itself, x.