A body of mass 1 kg begins to move under the action of a time dependent force `vec(F) =(2t hat(i)+3t^(2)hat(j))` N . Where `hat(i) and hat(j)` are unit vectors along X and Y axis . What power will be developed by the force at the time t .

Options

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

Answer

C

Explanation

`vec(F) =(2t hat(i)+3t hat(j))N ` and
`vec(a) =(vec(F))/m = (2t hat(i)+3t^(2) hat(j))ms^(-2)`
` :. V = int_(0)^(t) "a dt"`
` = int_(0)^(t) (2t hat(i)+3t^(2)hat(j)) dt`
` = [ t^(2) hat(i) +t^(3) hat(j)]_(0)^(t)`
`= t^(2) hat(i)+t^(3) hat(j)`
` :. ` Power `P = vec(F ) .vec(v)`
` = (2t hat(i) +3t^(2)hat(j)).(t^(2)hat(i)+t^(3)hat(j))`
` :. P = (2t^(3)+3t^(5))W`