This paper presents a principled approach to the modeling of human drivers-applied to stop behavior-by uniting recent ideas in cognitive science and optimal control. With respect to the former, we invoke the affordance competition hypothesis, according to which human behavior is produced by resolving the competition between action affordances that are simultaneously instantiated in response to the environment. From the theory of optimal control, we deploy motor primitives based on minimum jerk as the potential suite of actions. Furthermore, we invoke a layered control architecture, which carries out action priming and action selection sequentially, to model the biological affordance competition process. Motor output may be directed to distinct motor channels, which may be partially inhibited, e.g., to model gas pedal release saturation. Within this architecture, two types of motor units-"deceleration" acting on a gas pedal channel and "brake" acting on a brake pedal channel-are sufficient to model, with remarkable accuracy, the various phases that can be observed in human maneuvers in stopping a car, namely: gas release, gas chocked, brake, and final brake release at stop. The model is validated using experimental data collected in 16 different stop locations, from roundabouts to traffic lights. We also carry out a comparison with the well-known Intelligent Driver Model, discuss the scaling of this framework to more general driving scenarios and finally give an example application where the driver model is used, within a mirroring process, to infer the human driver intentions.