The analysis of the vehicle acceleration process is a current topic based on the aspects related to the general characteristics of the car, its parameters, design, drive unit performance, and the influence of external factors. Therfore in the article, the authors assessed the dynamic and energy parameters of the car motion, in which the intensity of acceleration of the car with different intensities was examined. Acceleration was carried out in two variants, the first for a normal internal combustion engine and the second for the same engine but additionally equipped with a short-term boost system. In this way, it influences the increase in power and energy in the car drive system, changing its acceleration intensity. Variable car acceleration intensity was obtained in the range from 0.12 to 1.37 m/s2 , and energy consumption at the level of 0.4 to 1.2 MJ in the distance of 1/4 mile. The article proposes a combination of energy parameters and engine power in order to assess the acceleration dynamics, for this purpose, the specific energy consumption of the car was determined, ranging from 0.35 to 2.0 J/(kg∙m), which was related to the engine power, denoting it with the dynamics index. The study focuses on the assessment of the relationship between the specific energy consumption and acceleration of passenger cars in the available powertrain system using a new dynamics index. The proposed dynamics index combines the energy and dynamic parameters of the car to be able to objectively quantify the acceleration process.