Rate of Doing work

Power is defined as the rate of doing work or the rate of transfer of energy.

Power (P) = Work done / Time taken

P = W/t

Where, P = Power

W = Work done

t = Time taken

SI unit of power is Watt (W)

1 Watt (W) = 1 Joule/1 second

= 1J/1s

Power is one Watt when one joule work is done in one second.

Average power = Total work done or total energy used/ Total time taken

1 Kilowatt = 1000 watts

1 kW = 1000 W

1 kW = 1000 J s^-1

The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time. Therefore the concept of average power is useful. We obtain average power by dividing the total energy consumed by the total time taken.

Ex:- A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm. Find his power. (g=10 m s^-2)

Sol:-Weight of boy (mg) = 50 kg × 10 m s^-2 = 500 N

height of staircase (h) = 45 × 15/100 m = 6.75 m

Total time taken (t) = 9 s

Power (p) = Work done / time taken

= mgh/t

= 500 N × 6.75 m/9s

= 375 W

Thus, the power is 375 W.