# 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,

• $W = \int_{t_{2}}^{t_{1}} P dt$