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Power supplied to a particle of mass 3 k...

Power supplied to a particle of mass 3 kg varies with time as `p = 4t ^(3)` watt, where t in time is seconds. If velocity of particle at `t =0s ` is ` u=2 m//s.` The velocity of particle at time `t =3s` will be :

A

`sqrt58 m//s`

B

`sqrt29m//s`

C

`sqrt87 m//s`

D

`sqrt27m//s`

Text Solution

Verified by Experts

The correct Answer is:
A
`W = K E _("final") -KE _("initial")`
`implies int _(0)^(3) Pdt =1/2 mV ^(2)-1/2 m u ^(2) " " implies int _(0)^(3) 4t ^(3) dt = 3/1V ^(2) - 3/2 xx4`
`implies 81 +6 = 3/2 V ^(2) " " implies 87 = 3/2 V ^(2)`
`implies ^(2) = 58" " V = sqrt58 m //s " " therefore1)`
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