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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

`sqrt29 m//s`

C

`sqrt87 m//s`

D

`sqrt27 m//s`

Text Solution

Verified by Experts

The correct Answer is:
A
`W-KE_("final")- KE_("initial")`
`rArr underset(0)overset(3)int Pdt = (1)/(2) mV^(2) - (1)/(2) m u^(2) rArr underset(0)overset(3)int 4t^(3) dt= (3)/(2) V^(2)- (3)/(2) xx 4`
`rArr 81 + 6= (3)/(2)V^(2) rArr 87 = (3)/(2)V^(2)`
`rArr V^(2) = 58 therefore V= sqrt58 m//s therefore` (1)
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