Currently on the market there is no vehicle in which the intelligent transportation systems (ITS) have not found application. One of the most developed ITS lately is the Adaptive Cruise Control (ACC). The ACC is a new technology which requires the use of sensors for detecting the speed and distance of the vehicle in front of a vehicle equipped with the ACC system and enables ACC vehicle to adjust its speed accordingly. In this paper we have developed an ACC model. Also, we have analyzed the results obtained by its simulation. The MATLAB program is used to solve the equations used for the formation of the ACC model. In this paper, a physical and mathematical model and simulation results are presented in the form of diagrams.