Problem. The disadvantage of current dependences for determining the acceleration indicators at engine maximum brake power and driving tire-to-surface friction coefficients is that they are adequate only if the engine and transmission parameters provide power input to the drive wheels rolling without slipping regardless to speed. To eliminate this drawback, it is necessary to take into account that the power input to the drive wheels depends on the engine shaft speed, and therefore on the speed of the vehicle when accelerating. Goal. The purpose of the work is to further develop the theory of the automobile by improving the dependencies that allow determining the automobile acceleration rates and assessing the nature of its acceleration process from the design factors. Methodology. The approaches taken to achieve this goal are based on laws of physics, theoretical mechanics and the theory of automobile. Results. Analytic dependences for determining maximum and limiting automobile acceleration when speeding up depending on its design factors and speed have been improved. Dependences for determining the range of drive wheel slipping on the automobile speed when accelerating and the limiting automobile acceleration under the condition of its pitch stability have been obtained. When studying the automobile acceleration process theoretically it was found that the developed dependences allow determining the nature of automobile movement and assessing the influence of its design factors on the acceleration indicators. Originality. The obtained dependences for determining the maximum and limiting acceleration, the range of driving speeds with wheel slip when automobile accelerating allowed us to clarify the idea of the nature of movement during acceleration and the influence of automobile design factors on the acceleration indicators. Practical value. The obtained dependences can be used in designing new and improving racing cars such as dragsters, and analysing the dynamics of the vehicle when accelerating with full fuel delivery and determining the nature of driving tire-to-surface friction depending on the driving speed.