A body of mass `6kg` is under a force which causes displacement in it given by `S= (t^(2))/(4)` maters where `t` is time . The work done by the force in `2` sec is

Options

A. `12 J`
B. `9 J`
C. `6 J`
D. `3 J`

Answer

D

Explanation

`s = (t^(2))/(4) :. Dx = (1)/(2) dt`
`F = ma = (md^(2)s)/(dt^(2)) = (6d^(2))/(dt^(2)) [(t^(2))/(4)] = 3N`
Now
W=underset(0)overset(2)intF.dS=underset(0)overset(2)intma.dS`
`underset(0)overset(2)int3xx2t xxt^(2)dt=underset(0)overset(2)int6t^(3)dt=(3)/(2)[t^(4)]_(0)^(2)=24J`.