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 prop 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`
Integrating `int_(0)^(v) vdv = int_(0)^(x) ((K_(0))/(m)) dx` ,
`(v^(2))/(2) = ((K_(0))/(m)) x rArr x = (1)/(2) (mv^(2))/(K_(0))`.