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)therefore ds = (t)/(2)dt`
`F = ma=(md^(2)s)/(dt^(2))=(6d^(2))/(dt^(2))[(t^(2))/(4)]=3N`
Now
`W= int_(0)^(2)F ds = int_(0)^(2)3(t)/(2)dt=(3)/(2)[(t^(2))/(2)]_(0)^(2)=(3)/(4)[(2)^(2)-(0)^(2)]=3J`