A body of mass `3 kg` is under a force , which causes a displacement in it is given by `S = (t^(3))/(3)` (in metres). Find the work done by the force in first `2` seconds.

Options

A. 2 J
B. 3.8 J
C. 5.2 J
D. 24 J

Answer

D

Explanation

`S=t^3/3`
`v =(dS)/(dt)=t^2 implies dS = t^2 dt`
Force (F) = ma = 3(2t) = 6t
`W = intFdS = int_(0)^2 (6t)(t^2 dt)`
`W=6int t^3 dt =6 [t^4/4]_0^2=24J`