The purpose of this paper is to show the effect of acceleration -variable forward velocity-, on the steady-state and transient responses of turning vehicles and the resulted path of motion of the vehicle. Comparing the responses of the vehicle will be used to prove that there is a negligible difference between the steady-state and transient center of rotation of the vehicle in engineering applications. To show that vehicles are working close to their steady-state conditions even at transient stage, we examine a vehicle in two maneuvers. In the first one, the vehicle is assumed to be moving at a constant forward speed and experiencing a step steer angle change. In the second maneuver, the vehicle experiences a lane change steering input. The transient response of the vehicle, as well as the required time to achieve the steady-state conditions will be analyzed.