A constant power P is applied on a particle of mass m. find kinetic energy, velocity and displacement of particle as function of time t.

Explanation

As is known, `P=Fv=(ma)v=m((dv)/(dt))v.`
`:. vdv=(P)/(m)dt`
Integrating both sides, we get
`(v^(2))/(2)=(P)/(m)t, v=sqrt((2P)/(m))t^(1//2)`
`v=(dx)/(dt)=sqrt((2P)/(m))t^(1//2) or dx=sqrt((2P)/(m))t^(1//2)dt`
Integrating both sides, we get
`x=sqrt((2P)/(m))(t^(3//2))/(3//2)=(2)/(3)sqrt((2P)/(m))t^(3//2)`
This is the required expression.