The position (x) of body moving along x-axis at time (t) is given by `x=3f^(2)` where x is in matre and t is in second. If mass of body is 2 kg, then find the instantaneous power delivered to body by force acting on it at `t=4` s.

Explanation

Instantaneous power `=vecF.vecv`
`F=ms=(mdv)/(dt)=(md)/(dt)((dx)/(dt))`
Find v `(=(dx)/(dt))` then find `vecFvecv.`
`x=3P`
`v=(dx)/(dt)=6t`
`a=(dv)/(dt)=6`
`F=ma=2xx6=12`
Instantaneous power at `t=4s=F.v=12(6xx4)`
`=288W`