This paper proposes a Combined Adaptive Velocity and Acceleration Control (CAVAC) aw for autonomous vehicles in the presence of unknown and uncertain parameters. In particular, the global asymptotic stability of the nonlinear vehicle system under the proposed adaptive velocity control is shown to be held without real-time estimation of the vehicle parameters. Moreover, the CAVAC law is applied to ensure the required inter-vehicle spacing, crucial to avoiding collisions in vehicle platoons. The simulation studies illustrate the advantages of the CAVAC law for the autonomous vehicle platoon in dealing with the speed limit changes, in mitigating issues induced by merging-exiting, and in ensuring collision avoidance. The experiments conducted on an electric vehicle also validate the effectiveness of the proposed control laws.