A body of mass 1 kg begins to move under the action of a time dependent force `vecF = (2 t hati + 3t^2 hatj)N`, where `hati` and `hatj` are unit vectors along x and y axis. What power will be developed by the force at the time?

Options

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

Answer

B

Explanation

Here , `vec(F) = (2t hati + 3 t^2 hatj) N, m = 1 kg`
Acceleration of the body , `vec(a) = (vecF)/m = ((2 t hati + 3t^2 hatj)N)/(1 kg)`
Velocity of the body at time t,
`vecv = int vec(a) dt = int (2 t hati + 3 t^2 hatj) dt = t^2 hati + t^3 hatj ms^^(-1)`
`:. ` Power developed by the force at time t.
`P = vecF . vecv = (2 t hati + 3 t^2 hatj) . (t^2 hati + t^3 hatj) W = (2 t^3 + 2t^5) W`.