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

Explanation

`P = Fv = mav = m ((dv)/(dt)) v`
`k = (mvdv)/(dt)`
`int_(0)^(v) v dv = (k)/(m) int_(0)^(t) dt`
`(v^(2))/(2) = (k)/(m) implies v = sqrt((2 k)/(m)) t^(1//2)`
`a = (dv)/(dt) = sqrt((2k)/(m)) (1)/(2) t^(-1//2) = sqrt((k)/(2 m)) t^(-1//2)`
`F = ma = m sqrt((k)/(2m)) t^(-1//2) = sqrt((mk)/(2)) t^(-1//2)`