# Power

Power of a body is defined as the rate at which the body can do the work.

Average power,

Instantaneous power,

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i.e., power is equal to the scalar product of force with velocity.

Important Points

- Relations between different units:
^{7}erg/s^{6}W^{3}W - If work done by the two bodies is same, then power ∝ 1/time, i.e., the body which performs the given work in lesser time possesses more power and vice versa.
- As power = work/time, any unit of power multiplied by a unit of time gives the unit of work (or energy) and not power, i.e., Kilowatt-hour or watt-day are units of work or energy.

- The slope of work–time curve gives instantaneous power (Fig. 14).
*P*=*dW/dt*= tan*θ*

**Fig. 14**

- Area under power–time curve gives the work done as
*P-t*curve