Abstract
The article has developed a unified theoretical system for determining the average velocity of a body, this value is discussed from a new perspective. In particular, the problem of determining the average velocity is expressed in the nature of replacing several uniform movements with one uniform movement or several arithmetic progressions of coordinates with one progression. Six different cases of determining the average speed are considered, a theoretical justification for each of them is developed and a quantitative analysis is carried out using exercises (examples) on them. The introductory part tells about the progressive prerequisites of smooth movement, it is proved that the average speed is the speed of coordinate change. The following sections cover several different body coordinate changes and the problems of combining them. The results of each situation under consideration are discussed and conclusions are drawn. A generalized formula for determining the average speed for each case under consideration. 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.