A machine delivers power to a body which is directly proportional to velocity of the body. If the body starts with a velocity which is almost negligible, find the distance covered by the body in attaining a velocity `v`.

Explanation

Power `P = Fv cos 0 = Fv = m((dv)/(dt)) v "infty" v`
`mv (dv)/(dt) = K_(0)v , Where K_(0) = constant`
`m (dv)/(dt) = K_(0), m((dv)/(dx)) dx/dt = K_(0)`
`mv dv/dx = K_(0), vdv = ((K_(0))/(m) dx`
Intefrating `int _(0)^(v) v dv = int_(0)^(x) (K_(0))/(m))dx `
`(v^(2))/2 = (K_(0))/(m) xx Rightarrow x = 1/2(mv^(2))/(K_(0))`