A body of mass 1 kg begins to move under the time dependent force `F= 2thati +3thatj` N, where are unit vectors along x and y axis. What power is developed by the force at the timet?

Options

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

Answer

D

Explanation

`vecF=2ti+3t^2hatj`
`m(doverlinev)/(dt)=2thati+3t^2hatj`
`overset(v)underset(o)(int)d overserlineV=overset(1)underset(0)(int)(2thati+3t^2hatj)dt=t^2hati+t^2hatj`
Power=`overlineF.overlineV=(2t^3+3t^5)W`