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)/(2)sqrt(mk)" t"^(-1//2)`

Answer

A

Explanation

(a)As jthe machine delivers a constant power So, F.v=constant =k(watts)
`rArr " " m(dv)/(dt).v=k rArr intvdv=(k)/(m)int dt`
`rArr " " (v^(2))/(2)=(k)/(m)trArrv=sqrt((2k)/(m)t)`
Now, force on the particle is given by
`F=m(dv)/(dt)=m(d)/(dt)((2kt)/(m))^(1/2)=sqrt(2km.)((1)/(2)t^(-1/2))=sqrt((mk)/(2)).t^(-1//2)`