Velocity smoothing is one problem which is proposed in high speed machining and coal mine safety production, the aim of which is to improve machining accuracy and equipment life. Aiming at this problem, this paper proposes a stage wise model and deduces the closedform expression solution for each stage based on the relationship of acceleration and velocity, and then deduces the general solutions of cubic equation in detail for the model. Finally, the solutions are applied to the velocity smoothing. The proposed schema shows the advantages of easy to program and smoothing in transition curve when being applied for velocity smoothing in coalmine. The result demonstrates that the proposed method adapts the highspeed scenarios well and has used in other several projects.