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{excerpt} *Power* is the time rate of change of doing [Work].{excerpt} The symbol often used for power is *P* . If work is denoted by *W* , then
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{latex}\begin{large} \[P \equiv \frac{dW}{dt} \]\end{large}{latex}
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Since work is [force] exerted over [displacement], the work done by a constant force over a displacement is given by
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{latex}\begin{large} \[ W = \vec{F} \cdot \vec{r} \]\end{large}{latex}
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If the force is constant, then its derivative with respect to time is zero. and we have
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{latex}\begin{large} \[ P = \frac{dW}{dt} = \vec{F} \cdot \frac{d{\vec r}}{dt} \]\end{large}{latex}
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