The derivative of the position function is the ______ function.

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

Answer: (D)

The derivative of position with respect to time is velocity. Position tells you where you are, and taking its rate of change shows how fast that location is changing and in what direction. If position is a vector r(t), then velocity is v(t) = r′(t), a vector that captures both speed and direction. The speed you hear about is only the magnitude of velocity, a scalar. Acceleration would be the derivative of velocity (the second derivative of position), and jerk is the derivative of acceleration (the third derivative). So the derivative of the position function is the velocity function. For a quick example, if s(t) = t^2 meters on a straight line, then velocity is ds/dt = 2t meters per second.