This article proposes a path following controller for the two input kinematic model of a car-like robot. A smooth dynamic feedback control law is designed to make the car's position follow a large class of curves with the desired speed along the curve. The controller guarantees the property of path invariance. The controller is designed by characterizing the path following manifold when one input is fixed. Once the path following manifold is found we apply dynamic extension to increase its dimension. We refer to this process as tangential dynamic extension. We then find a physically meaningful differentially flat output for the extended system which allows us to easily solve the path following problem.