AP Calculus BC Practice Test

Acceleration is the rate of change of velocity, so for a particle with position r(t) = (x(t), y(t)), its velocity is v(t) = r'(t) = (x'(t), y'(t)). The acceleration is the derivative of velocity, a(t) = v'(t) = r''(t) = (x''(t), y''(t)). Thus the acceleration vector has components given by the second-time derivatives of the coordinates. The first derivatives (x'(t), y'(t)) are velocity, the original position (x(t), y(t)) is position, and the third derivatives (x'''(t), y'''(t)) relate to jerk.