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A body of mass 6kg is under a force whic...

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

A

12 J

B

9 J

C

6 J

D

3 J

Text Solution

Verified by Experts

The correct Answer is:
D
`s=(t^2)/(4)`
`ds=(t)/(2)dt`
`F=ma=(md^2s)/(dt^2)=(6d^2)/(dt^2)[(t^2)/(4)]=3N
Now `W=int_0^2Fdsint_0^23(t)/(2)dt=(3)/(4)[(2)^2-(0)^2]=3J`
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