An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P. Find its position and instantaneous velocity at time t assuming the automobile starts from rest.

Explanation

`t=0`,`v=0`,`s=0`
`P=Fv=mav=m(dv)/(dt)v`
`int_(0)^(v)vdv=(P)/(m)int_(0)^(t)dt`
`(v^2)/(2)=(P)/(m)t`
`v=sqrt((2P)/(m))t^((1)/(2))`
`(ds)/(dt)=sqrt((2P)/(m))t^((1)/(2))`
`int_0^(S)ds=sqrt((2P)/(m))int_0^(t)t^((1)/(2))dt`
`s=sqrt((2P)/(m))(t^((3)/(2)))/((3)/(2))=(2)/(3)sqrt((2P)/(m))t^((3)/(2))`
`=sqrt((8P)/(9m))t^((3)/(2))`