Problem. During the study of the circumstances of the occurrence of road floors, the experts of the automotive technical expertise have a question about the choice of mathematical model for determining the deceleration of a two-axle vehicle with a faulty working brake system. The search for a universal method for calculating the amount of deceleration of a two-axle vehicle with a faulty working brake system is an urgent scientific task that will expand the understanding of the physical processes on which the provisions of the theory of the car are based. Goal. The aim of the work is to generalize theoretical research to determine the deceleration of a two-axle vehicle with a faulty working brake system. Methodology. The approaches adopted in the work to solve this goal are based on the analysis of methods for determining the deceleration of two-axle wheeled vehicles. Results. The obtained calculated values of deceleration of a two-axle wheeled vehicle with different external factors allowed to establish the features of the use of different methods in the practice of automotive technical expertise. It is established that taking into account the angle of the road surface towards the roadside and taking into account the coefficient of resistance of car tires can change the amount of deceleration of a two-axle wheeled vehicle with a faulty service brake system. Originality. The proposed universal method for determining the deceleration of a two-axle wheeled vehicle with a faulty working brake system, allows to take into account the influence of rolling resistance of tires and the angle of inclination of the road surface towards the roadside when studying the circumstances of a traffic accident. Practical value. The results obtained can be recommended in the practice of automotive technical expertise or in research related to determining the braking performance of two-axle wheeled vehicles.

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Problem. The disadvantage of the existing dependencies for determining the possibility of the automobile drive wheel slip with the maximum use of engine power and indicators of the interaction of the drive wheels with the supporting surface is that they are correct only if the motion of the car is steady. This downside is due to the fact that when deriving the equation of the car motion, the assumption is made that the total tractive force is on the drive wheels, that is, without taking into account the energy losses due to the increase in the kinetic energy of the rotating masses of the engine, transmission, and drive wheels. At the same time, the specified energy losses are compensated by a relative increase in the inertia (mass) of the gradually moving car. Such an assumption is quite correct for determining the traction and speed characteristics of a car not only during steady motion but also during acceleration. Determining the possibility of the automobile drive wheel slip during automobile acceleration, this assumption is incorrect because the drive wheels are not affected by the total tractive force, but by a force that is reduced in accordance with energy losses due to an increase in the kinetic energy of the rotating masses of the engine, transmission, and driving wheels. It is necessary to take into account the reduction of the tractive force on the drive wheels during the acceleration of the car in order to eliminate the mentioned shortcoming. Goal. The aim is the further development of the theory of the car by improving the dependencies that allow determining the conditions for the possibility of the automobile drive wheel slip during its acceleration and the modes of its motion. Methodology. The considered approaches for achieving this aim are based on the laws of physics, theoretical mechanics and provisions of the theory of the car. Results. Analytical dependencies have been improved to determine the conditions for the possibility of the automobile drive wheel slip during its acceleration and the modes of its motion. Dependencies for determining the range of the automobile drive wheel slip on the speed of the vehicle during acceleration are obtained. During the theoretical study of the car motion process, it was established that the developed dependencies allow determining the car driving mode and the possibility of the automobile drive wheel slip both during acceleration and steady motion. Originality. The obtained dependences for determining the possibility of the automobile drive wheel slip during acceleration of the car made it possible to clarify the idea of ​​the driving mode of the car and the possibility of the automobile drive wheel slip both during acceleration and during steady motion. Practical value. The obtained dependencies can be used in the design of new and improved sports cars such as dragsters, and for analyzing the dynamics of the car motion during acceleration with total fuel supply and determining the nature of the interaction of the drive wheels with the supporting surface depending on the speed of motion.