In this article, uniform rectilinear motion is considered as an increasing or decreasing mathematical progression of the coordinates of the body, and its change to an uneven (accelerated) movement as a violation (deviation) of the progression. It is also shown that when the time coordinate changes deviate from a uniform position, the rate of progression and movement of the body in each second become a growing or decreasing progression. The mathematical integrity of the first Newton's law is determined, which is intended to consider changes in the coordinates of the body according to the linear law and the second Newton's law, which considers the change of coordinates according to the law of the parabola. The mathematical justification (theoretical) of uniform and uneven motion is given by graphical and physical representation of these quantities, considering changes in mechanical quantities (coordinates, velocities, displacements) over time as linear and nonlinear functions.