There is not a unified answer to the question “is there a physical substrate of motion?”. On one hand, any moving body has a momentum, e.g., amount of motion, whose magnitude is defined by the motion speed and body mass. On the other hand, neither classical nor relativistic physics have a positive answer to the above question and describe the physical substrate of motion or momentum. According to the author's concept a zone (space area) is formed behind each elementary particle where chaos is disturbed and there is a preferred motion direction (PMD) of graviton- pulses since they are driven to the formed space as a result of a particle movement. The author refers to this zone, which represents a flow of graviton-pulses towards the motion direction, as the acceleration zone. This zone discerns material particles in motion (that obtained an acceleration momentum) from still particles. The magnitude of the latter is directly proportional and corresponds to the speed of motion