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

Options

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

Answer

A

Explanation

`m=1kg`
`a=(F)/(m)=(2t)/(1)hati+(3t^(2))/(1)hatj`
Velocity `v=int adt`
`=int2t dt hati+int3t^(2)dthatj`
`=t^(2)hati+t^(3)hatj`
Power `P=F.V`
`(2thati+3t^(2)hatj).(t^(2)hati+t^(3)hatj)`
`=(2t^(3)+3t^(5))w`