A concise self-closed way to the acceleration formula for the moving frame

The motion analysis of a particle in a moving frame is very important in courses of both physics and engineering mechanics. Nonetheless, the narrations in most textbooks are not completely satisfactory. This report suggests a concise approach to derive the acceleration formula for a moving frame. The suggested approach, starting from the unit moving vector, is self-closed. The deduction makes uses of the vector, which leads to a clear image of the Coriolis acceleration.