Power supplied to a mass 2 kg varies with time as `P = (3t^(2))/(2)` watt. Here `t` is in second. If velocity of particle at `t = 0` is `v = 0`, the velocity of particle at time `t = 2s` will be:

Options

A. `1 m//s`
B. `4 m//s`
C. `2 m//s`
D. `2 sqrt2 m//s`

Answer

C

Explanation

From work energy thorem,
`Delta KE = W_("net")` or` K_(f) - k_(i) = int Pdt`
`Delta KE = W_("net")` or `K_(f) - k_(i) = int Pdt`
or `(1)/(2)mv^(2) - 0 = int_(0)^(2) ((3)/(2) t^(2)) dt or v^(2) = [(t^(3))/(2)]_(0)^(2)`
or `v = 2m//s`