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The position (x) of body moving along x-...

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.

Text Solution

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