Power

Power is the measure of how much work is done per unit time or the rate of change of work done. It is the total work done by a force divided by the time interval during the work is done. Let $s$ is the total displacement covered by a body under the action of a constant force of magnitude $F$ in the direction of displacement in time interval $\Delta t = {t_2} - {t_1}$. Then, the power is the total work done divided by the time interval that is,

\[P = \frac{{Fs}}{{{t_2} - {t_1}}} = \frac{W}{{\Delta t}}\]

In case of a variable force or the displacement is not along a straight line we can find the rate of change of work done at any particular instant. Let $dW$ is a very small work done in a very small time interval $dt$ in which $\Delta t$ approaches zero. Note that in a very small time $dt$ the force can be taken as constant and the displacement is also along a straight line, so the power at any instant is,

\[P = \frac{{dW}}{{dt}} \tag{4} \label{4}\]

The SI unit of power is watt denoted by $\text{W}$ which is $\text{J/s}$ or $\text{kg} \cdot \text{m}^2/\text{s}^3$. Note that the unit of power and work done denoted by the same letter $\text{W}$ are not the same things.

Mechanics
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