Where did you get this ?

Integrating both sides we get, as given that at distance x=4, v=0 and at x=12 v=V. S dx = S mvdv 4-umg kV 2 16 12 V dx = mvdv 4-umg kV 2 O 16 substitute, 4 - umg - KV 2 16 = 2kvdv = 16dt vdv = 5dt for limit V = 0, t =4 - umg V = V, t =4 - umg kV 2 16