Power quantifies how quickly work is done.
We can define average power as the ratio
$$ P_{\mathrm{av}}=\frac{\Delta W}{\Delta t} $$ and the instantaneous power as the limit $$ P=\lim _{\Delta t \rightarrow 0} \frac{\Delta W}{\Delta t}=\frac{d W}{d t} $$ Using the fundamental theorem of calculus, the instantaneous power can also be expressed as $$ P=\frac{d W}{d t}=\frac{d }{d t}\int \vec F\cdot d\vec r=\frac{d }{d t}\int \vec F\cdot \vec v dt \implies P=\vec F\cdot\vec v $$ The SI unit of power is the watt (W), in honor of the English inventor James Watt. $1 \mathrm{W}=1 \mathrm{J} / \mathrm{s}$
Potential Energy