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A body of mass 3 kg is under a force , w...

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.

A

2 J

B

3.8 J

C

5.2 J

D

24 J

Text Solution

Verified by Experts

The correct Answer is:
D
`S=(t^3)/(3)` `Ds=t^2dt`
`a=(d^2S)/(dt^2)=(d^2)/(dt^2)[(t^3)/(3)]=2t(m)/(s^2)`
Now work done by the force `W=int_0^2FdS=int_0^2madS`
`int_0^23xx2txxt^2dt=int_0^26t^3dt=(3)/(2)[t^4]_0^2=24J`
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