Derivative

In mathematics, the derivative is one of the two central concepts of calculus. (The other is the integral; the two are related via the fundamental theorem of calculus.)

Physics

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:

Related Topics:
Physics - Newtonian physics

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• 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) = -16t^2 + 16t + 32; then, the object's velocity is dot p(t) = p'(t) = -32t + 16; the object's acceleration is ddot p(t) = p(t) = -32; and the object's jerk is p(t) = 0.

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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.

Related Topics:
Velocity - Car - Time - Acceleration

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