Question

Power supplied to a mass `2 kg` varies with time as `P = (3t^(2))/(2)` watt. Here `t` is in second . If velocity of partical at `t = 0 is v = 0`, the velocity of partical at time `t = 2s` will be:
A. `1 m//s`
B. `4 m//s`
C. `2 m//s`
D. `2 sqrt2 m//s`

Answer 1

Correct Answer - C
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`