A body of mass `m` is acceleratad uniformaly from rest to a speed `v` in a time `T` . The instanseous power delivered to the body as a function of time is given by

Options

A. `(1)/(2) m (v)/(t_(1)) t^(2)`
B. ` m (v)/(t_(1)) t^(2)`
C. `(1)/(2) ((mv)/(t_(1))) ^(2) t^(2)`
D. `(1)/(2) mv^(2) ((t)/(t_(1))) ^(2)`

Answer

D

Explanation

`a = v//t_(1)`. Displacement after time `t` :
`S = (1)/(2) at^(2) = (1)/(2) (v)/(t_(1)) t^(2)`
`W = FS = maS = m (v)/(t_(1)) (1)/(2) (v)/(t_(1)) t^(2) = (1)/(2) m v^(2) ((t)/(t_(1)))^(2)`