Mechanics: Chapter 15 – Power

Power is the rate of work done.

  • P = \frac{W}{\Delta t} = \frac{dW}{dt}

Since a infinitesimal amount of work done dW = F \cdot ds,

  • P = \frac{dW}{dt} = \frac{F \cdot ds}{dt} = F \cdot \frac{ds}{dt} = \overrightarrow{F} \cdot \overrightarrow{v}

Hence, power is also the dot product of the Force and the velocity of the object. In other words,

  • P = Fvcos(\theta)

Similarly, because of the fundamental theorem of calculus,

  • W = \int_{t_{2}}^{t_{1}} P dt
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