A body of mass 1kg begins to move under the action of a time dependent force `vecF =(2thati+3t^2hatj)N` where `hati and hatj` 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

Acceleration of the particle at time t,
`veca=(vecF)/m=(2thati+3t^2hatj)/1=(2thati+3t^2hatj)m//s^2`
Velocity of the particle at time t,
`vecv=int_0^tvecadt=int_0^t(2thati+3t^2hatj)dt=(t^2hati+t^3hatj)m//s`
Power developed by the force at time t,
`P=vecF*vecv=(2thati+3t^2hatj)*(t^2hati+t^3hatj)=(2t^3+3t^5)W`