Power

Rate of work done

P=Wtpower=work donetime\begin{align*} P &= \frac{W}{t} \\ \text{power} &= \frac{\text{work done}}{\text{time}} \end{align*}

Unit of PP = W\mathrm{W}
Unit of PP = J s−1\mathrm{J\,s^{-1}}

Instantaneous power

P=Fvpower=forceâ‹…velocity\begin{align*} P &= Fv \\ \text{power} &= \text{force} \cdot \text{velocity} \end{align*}

Power and velocity varies over time

Efficiency

η=EoutEin=PoutPinefficiency=useful input energytotal input energy=useful input powertotal input power\begin{align*} \eta &= \frac{E_\text{out}}{E_\text{in}} = \frac{P_\text{out}}{P_\text{in}} \\ \text{efficiency} &= \frac{\text{useful input energy}}{\text{total input energy}} = \frac{\text{useful input power}}{\text{total input power}} \end{align*}