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

Answer

D

Explanation

`(dW)/(dt) = P`
`W = Pt =1/2 mv^2`
So, `sqrt((2Pt)/(m)) = v`
Hence `a = (dv)/(dt) = sqrt((2P)/m). 1/(2sqrtt)`
So , Force `sqrt((2Pm^2)/m).(1)/(2sqrtt)=sqrt((Pm)/(2t))= sqrt((Km)/2)t^(-1//2)`
[Here P = K is given ]