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A body of mass 3 kg is under a constant ...

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

A

`5/19J`

B

`19/5J`

C

`8/3J`

D

`3/8J`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `x=3t-4t^(2)+t^(3) and" velocity "=(dx)/(dt)=3-8t+3t^(2) ........(1)`
`therefore` Velocity at t=0 is given by `v_(1)=3-0+3=3m//s` and veloocity at t=4 is given by
`v_(2)=3-8 xx 4+3 xx 4^(2)=19m//s`
Work done in time interval of 0 to 4s =Increase in K.E. `=1/2mv_(2)^(2)-1/2mv_(1)^(2)=1/2m(v_(2)^(2)-v_(1)^(2))`
`=1/2 xx 3 xx 10^(-3) (19^(2)-3^(2))=3/2 xx 10^(-3) (22 xx 16)`
`=3/2 xx 10^(-3) xx 352 =528 xx 10^(-3)J`
`therefore W=528J`
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