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Time derivative
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Everything about Time Derivative totally explained

A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t,.

Notation

A variety of notations are used to denote the time derivative. In addition to the normal notation, » frac = [-x(t),-y(t)] = - vec r (t) ,

showing that the acceleration is inward directed, exactly opposite in direction to the displacement vector, and orthogonal to the velocity vector. This inward directed acceleration can be provided by gravitational attraction, for example, as in the case of the earth and moon, and is called centripetal acceleration.

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