A partical of mass `m` is driven by a machine that deleveres a constant power `k` watts. If the partical starts from rest the force on the partical at time `t` is

Options

A. `sqrt((mk)/2) t^(-1//2)`
B. `sqrt(mk) t^(-1//2)`
C. `sqrt(2mk) t^(-1//2)`
D. `1/2sqrt(mk)t^(-1//2)`

Answer

C

Explanation

`P=("work")/("time") =k `
Power `= (dW)/(dt) = k ` , (start from rest )
`DeltaK.E = W = kt `
`-0 + 1/2 mv^(2) = kt rArr v = sqrt((2kt)/m)`
`a = (dv)/(dt) =1/(2sqrt((2kt)/m)) ((2k)/m)`
Force , `F = ma = 1/(2sqrt(t))sqrt(2mk) = 1/2 sqrt(2mk ) =1/2 sqrt(2mk)t^(-1/2)`
`=sqrt((mk)/2) t^((-1)/2)`