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

Explanation

`vec F = 2 t hat i + 3 t^(2) hat j`
`vec a = (d vec v)/(dt) = 2 t hat i + 3 t^(2) hat j`
`int_(0)^(vec v) d vec v = int_(0)^(t) (2t hat i + 3 t^(2) hat j) dt`
`vec v = t^(2) hat i + t^(3) hat j`
`rho = vec F * vec v = (2 t^(3) + 3 t^(5)) W`