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We present the design of a safe Adaptive Cruise Control (ACC) which uses road grade and lead vehicle motion preview. The ACC controller is designed by using a Model Predictive Control (MPC) framework to optimize comfort, safety, energy-efficiency and speed tracking accuracy. Safety is achieved by computing a robust invariant terminal set. The paper presents a novel approach to compute such set which is less conservative than existing methods. The proposed controller ensures safe inter-vehicle spacing at all times despite changes in the road grade and uncertainty in the predicted motion of the lead vehicle. Simulation results compare the proposed controller with a controller that does not incorporate prior grade knowledge on two scenarios including car-following and autonomous intersection crossing. The results demonstrate the effectiveness of the proposed control algorithm.