The purpose of this study is to clarify the jet tip velocity and mixing process between the jet and its surrounding fluid. The analysis was made with the time history of injection velocity which monotonously rises up just after the opening of injection valve and is steady later. The jet is injected into quiescent ambient air. The jet tip velocity first increases, then decreases, increases and last decreases with time lapses from injection. Therefore, the growing process of the jet is composed of four periods from the standpoint of the jet tip velocity. The jet tip velocity is maximum at the time boundary between the first and second growing periods, when the rate of increase of the injection velocity is maximum. The mixture between the jet and surrounding fluid is very active at this time. The growing period between the first period to the initiation of the fourth period corresponds to the unsteady period of injection velocity.