A body is moved along a straight line by a machine delivering constant power . The distance moved by the body is time `t` is proptional to

Options

A. `t^((1)//(2))`
B. `t^((3)//(4))`
C. `t^((3)//(2))`
D. `t^2`

Answer

C

Explanation

`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((2Pt)/(m))`
`(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))`
`spropt((3)/(2))`