A body of mass `1 kg` begins to move under the action of a time dependent force `vec F = (2 t hat I + 3 t^(2) hat j) N`, where `hat i` and `hat j` are unit vectors along x-and y-axes. What power will be developed by the force at the time `t` ?

Options

A. `(2t^2 +3t^3)W`
B. `(2t^2 +4t^4)W`
C. `(2t^3 +3t^4)W`
D. `(2t^3 +3t^5)W`

Answer

D

Explanation

`a=F/m = 2t hati + 3t^2 hatj`
`v = intadt = t^2 hati+t^3 hatj`
`P = vecf.vecc=2t^3 hati +3t^5 hatj`