A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation `s=1/3t^2` , where t is in seconds. Work done by the force in 2 seconds is:-

Options

A. `5/19J`
B. `3/8J`
C. `8/3J`
D. `19/5J`

Answer

C

Explanation

By using work energy theorem
`W=DeltaKE=(1)/(2) mv_(2)^(2)-(1)/(2) mv_(2)^(2)`
Now`s=(1)/(3)t^(2) impliesv=(2)/(3)t` `impliesv_(1)=0,v_(2)=(2)/(3)xx2=(4)/(3)ms^(-1)`
Therefore W`(1)/(2)xx3((4)/(3))^(2)-(1)/(2)xx3xx(0)^(2)=(8)/(3)J`