A car drives along a straight level frictionless road by an engine delivering constant power. Then velocity is directly proportional to

Options

A. `sqrt((2Pt)/(m))`
B. `(2Pt)/(m)`
C. `sqrt((2Pt)/(2m))`
D. `(Pt)/(2m)`

Answer

A

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))`