Power supplied to a particle of mass 2 kg varies with time as `P =(3t^2)/2W`, where t is in seconds. If velocity of particle at t=0 is zero, then the velocity of particle at t=2 s will be

Options

A. 1 m `s^(-1)`
B. 4 m `s^(-1)`
C. `2 m s^(-1)`
D. `2sqrt2 m s^(-1)`

Answer

C

Explanation

From work energy theorem , `Delta` K.E.=`W_"net"`
`therefore K_f-K_i = int P dt`
`rArr 1/2 mv^2-0 = int_0^2 (3/2t^2) dt rArr 1/2(2) v^2=3/2 [t^3/3]_0^2 =4`
`therefore` Velocity of the particle at t=2 s will be , v=2 m `s^(-1)`