The work done in time t on a body of mass m which is accelerated from rest to a speed v in time `t_1` as a function of time t 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 m (v^2)/(t_1^2) t^2`

Answer

D

Explanation

As `v = u + at = 0 + at_1 " " ( :. u = 0)`
`:. A = (v)/(t_1) " " ….(i)`
Force , `F = ma = (mv)/(t_1) `
Distance travelled by the body in time t is
`s = ut + 1/2 at^2 = 0 + 1/2 (vt^2)/(t_1) = (vt^2)/(2t_1) " (Using (i))"`
`:. W = F xx s = (mv)/(t_1) (vt^2)/(2t_1) = 1/2 (mv^2 t^2)/(t_1^2)`