In this paper, the Model Predictive Control (MPC) structure is used to solve the ACC problem and the performance of the design is tested using a realistic nonlinear vehicle model. A hierarchical control structure is used where MPC is placed on top of the hierarchy while the actuators are controlled by simpler linear controllers. The real-time optimization needed for MPC is solved using Quadratic Programming (QP). The performance of the MPC is tested under different traffic scenarios. The control system is able to determine the ongoing scenarios autonomously, using available measurements.