A particle of mass m, moving with a constant acceleration , acquires a velocity `v_0` in time `t_0` . Initially the particle was at rest. Find the average power and the instaneous power of the applied force.

Explanation

Work done on the particle in time `t_0 (W) ` Kinetic energy gained in `t_0 s =1/2 mv_0^2`
Hence, average power `= (1/2 mv_0^2)/(t_0) =(mv_0^2)/(2t_0)`.
If the velocity after a time t is v , then instantaneous power at a time t,
`P=(dW)/(dt) =d/(dt) (1/2 mv^2) =mv (dv)/(dt) =(mv^2)/t` [ as for a constant acceleration `(dv)/(dt) =v/t`]