One approach to motion control of autonomous vehicles is to divide control between path planning and path tracking. This paper introduces an alternative control framework that integrates local path planning and path tracking using model predictive control (MPC). The controller plans trajectories, consisting of position and velocity states, that best follow a desired path while remaining within two safe envelopes. One envelope corresponds to conditions for stability and the other to obstacle avoidance. This enables the controller to safely and minimally deviate from a nominal path if necessary to avoid spinning out or colliding with an obstacle. A long prediction horizon allows action in the present to avoid a dangerous situation in the future. This motivates the use of a first-order hold discretization method that maintains model fidelity and computational feasibility. The controller is implemented in real-time on an experimental vehicle for several driving scenarios.