Usage of differentiation

Arguably the most important application of calculus to physics is the concept of the "time derivative" — the rate of change over time — which is required for the precise definition of several important concepts. In particular, the time derivatives of an object's position are significant in Newtonian physics:

• Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with respect to time) of an object's position.
• Acceleration is the derivative (with respect to time) of an object's velocity.
• Jerk is the derivative (with respect to time) of an object's acceleration.

For example, if an object's position p(t) = - 16t² + 16t + 32; then, the object's velocity is ; the object's acceleration is ; and the object's jerk is p'''(t) = 0.

If the velocity of a car is given, as a function of time; then, the derivative of said function with respect to time describes the acceleration of said car, as a function of time.