This paper studies the simulation and control of an autonomous dragster. Four scenarios are provided that are critical to vehicle and driver safety in drag racing. Equations are then created to model the behavior during these safety scenarios. The use of a kinematic bicycle model and a Newtonian wheel stand model are discussed for plane-of-motion and out-of-plane vehicle movement, respectively. A separate controller is designed for each model by comparing different control methods. Proportional-Integral-Derivative (PID) control, optimal control, and model predictive control (MPC) are presented and applied to the models. The models are simulated from a speed of 75 m/s, being the estimated top speed of the research vehicle, up to a top speed of 150.5 m/s which is in alignment with the highest recorded speed of a dragster. The comparison of the control techniques yields MPC as superior for the bicycle model and PID as sufficient for the wheel stand model. Latency of the system is also discussed and accounted for in the system.