Autonomous cars and car-like robots have gained huge popularity recently due to the recent advancements in technology and AI industry. Motion and path planning is one of the most fundamental problems for such systems. In the literature, kinematic models are widely adopted for planning and control for these type of robots due to their simplicity (control and analysis) and fewer computational requirements. Though, applicability of kinematic models are limited to very low speeds or some specific cases, which can be easily violated in real life scenarios. Furthermore, most of the dynamical car models found in the literature assume that they are driven only in forward direction, at constant high speeds. In this study, we present a car model that captures the dynamics of both forward and backward driving, at low and high speeds. After creating the car model, we addressed the motion planning problem on this model, where we adopted a framework which combines Sequential Composition of Controllers (SCC) and Rapidly Exploring Random Trees (RRT). We performed simulations to show the effectiveness and robustness of our method, and results are promising for future experimental studies.