A particle of mass m id driven by a machine that delivers a constant power k watts . If the particle starts from at rest the force on the particle at time t is :

Options

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

Answer

D

Explanation

`P = FFv " Now ,F = ma"`
`K = ma " " = m((2k)/m)^(1/2)xx1/2t^(-1/2)`
`K = mv (dv)/(dt) " " = ((mk)/2)^(1/2).t^(-1/2)`
`K/m .dt = vdv " " = sqrt((mk)/2).t^(1/2)`
Integrating on both sides
`int k/m dt = int vdv`
`k/m t =(v^(2))/2 `
` :. v = sqrt((2k)/mt)`
`a = (dv)/(dt)=d/(dt)[((2k)/mt)^(1/2)]`
`:. a =((2k)/m)^(1/2) xx1/ 2t^(-1/2)`