In emergency situations, autonomous vehicles will be forced to operate at their friction limits in order to avoid collisions. In these scenarios, coordinating the planning of the vehicle's path and speed gives the vehicle the best chance of avoiding an obstacle. Fast reaction time is also important in an emergency, but approaches to the trajectory planning problem based on nonlinear optimization are computationally expensive. This paper presents a new scheme that simultaneously modifies the desired path and speed profile for a vehicle in response to the appearance of an obstacle, significant tracking error, or other environmental change. By formulating the trajectory optimization problem as a quadratically constrained quadratic program, solution times of less than 20 milliseconds are possible even with a 10 second planning horizon. A simplified point mass model is used to describe the vehicle's motion, but the incorporation of longitudinal weight transfer and road topography mean that the vehicle's acceleration limits are modeled more accurately than in comparable approaches. Experimental data from on an autonomous vehicle in two scenarios demonstrate how the trajectory planner enables the vehicle to avoid an obstacle even when the obstacle appears suddenly and the vehicle is already operating near the friction limits.