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This paper focuses on development of a dynamic model for an Ackermann-like vehicle based on a static tire-road friction model and laws of technical mechanics. The model takes as input the steering angle of the wheels in front and the rotational velocities of the drive wheels in the back of the vehicle. It delivers a 3-DOF output in terms of CoG vehicle velocity, body slip angle and the yaw rate of the vehicle in the x-y plane, as well as estimates on the forces acting on the system. It is suitable for modeling dynamic vehicle regimes in e.g. overtaking maneuvers/obstacle avoidance and lane-keeping, enabling active steering control by stabilizing the dynamics of the vehicle. The physical model description is based on previous works combined with a suitable friction model that is tractable in practice. Experimental verification of the obtained model is given for the Smart testing vehicle platform, where a separate analysis is done for directly measured as opposed to estimated/optimized parameters of the model.