Over the past years, car-like mobile robots (CLMRs) have been researched and developed for intelligent logistics systems in industrial environments and commercial applications, such as self-driving cars. A critical challenge lies in developing a dynamic model that accurately describes the interaction between CLMR and its environment during autonomous movement while following a desired motion trajectory. Hence, this paper focused on modelling and simulating the dynamics of CLMR while tracking a motion trajectory. First, the inverse kinematic and dynamic model of CLMR are established with velocity constraints to ensure that CLMR does not experience lateral and longitudinal slip. Moreover, factors such as wheel friction against the road surface and the CLMR’s inertial forces during movement are also considered. Then, the dynamic problem is computed and simulated to ensure the CLMR moves along a general trajectory in the Simulink/Matlab. The research results of this paper are important in proposing a new nonlinear controller design for CLMR to achieve high trajectory tracking accuracy at a certain speed. Additionally, they facilitate the development of semi-physical models, enabling the verification of proposed new controllers in scenarios where no physical model is available for experimentation.