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 b

Options

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

Answer

A

Explanation

(a) Work done `="Force"xx"displacement"`
F=ma and `s=(1)/(2)at^(2)`
Using,`" " s=ut+(1)/(2)at^(2)`
`:. " " W=maxx(1)/(2)at^(2)=(1)/(2)ma^(2)t^(2)`
`=(1)/(2)m((v)/(t_(1)))^(2)t^(2)=(1)/(2)m(v^(2))/(t_(1)^(2))t^(2) " " ("Using" a=(v)/(t_(1)))`