Write a note on Power.

(N/A) The time rate of doing work is known as power.
Power is defined as the work done per unit time or the time rate at which work is done or energy is transformed.
If $\Delta W$ is the work done in time interval $\Delta t$,the average power in time interval $\Delta t$ is $\langle P \rangle = \frac{\Delta W}{\Delta t}$.
Therefore,the instantaneous power at time $t$ is:
$P = \lim_{\Delta t \rightarrow 0} \frac{\Delta W}{\Delta t} = \frac{dW}{dt} \quad (1)$
If $dW$ is the work done by a force $\vec{F}$ during the displacement $d\vec{r}$,then $dW = \vec{F} \cdot d\vec{r}$.
Substituting the value of $dW$ in equation $(1)$:
$P = \frac{d}{dt}(\vec{F} \cdot d\vec{r}) = \vec{F} \cdot \frac{d\vec{r}}{dt} \quad [\because \vec{F} \text{ is constant}]$
$P = \vec{F} \cdot \vec{v} \quad [\because \frac{d\vec{r}}{dt} = \vec{v}]$
Power is a scalar quantity. Its dimensional formula is $M^{1} L^{2} T^{-3}$. The $SI$ unit of power is $J s^{-1}$. This unit is named as $watt$ in honor of the inventor of the steam engine,James Watt.
$1 W = 1 J s^{-1}$.
Larger units of power include:
$1 kW = 10^{3} W, 1 MW = 10^{6} W$.
To measure the power of vehicles and water pumps in practice,horsepower $(hp)$ is used,which is a unit of the British system.
$1 hp = 746 W$.