Adaptive Cruise Control (ACC) is now a common feature of production vehicles, and as such systems spread, the way they are tested, and the comfort of the driving they produce, has become as important as the control laws behind them. This thesis investigates the longitudinal control of an ACC-equipped vehicle and compares two control strategies, a classical Proportional-Integral (PI) controller and a Model Predictive Controller (MPC), with particular attention to ride comfort. The work is built on a non-linear longitudinal vehicle model developed in MATLAB/Simulink, which serves both as the plant under control and, in linearised form, as the internal model the MPC uses to predict the vehicle's response.