MPC (Model Predictive Control) techniques, with constraints, are applied to a nonlinear vehicle model for the development of an ACC (Adaptive Cruise Control) system for transitional manoeuvres. The dynamic model of the vehicle is developed in the continuous-time domain and captures the real dynamics of the sub-vehicle models for steady-state and transient operations. A parametric study for the MPC method is conducted to analyse the response of the ACC vehicle for critical manoeuvres. The simulation results show the significant sensitivity of the response of the vehicle model with ACC to controller parameter and comparisons are made with a previous study. Furthermore, the approach adopted in this work is believed to reflect the control actions taken by a real vehicle.