Stability and the string stability of a platoon of adaptive cruise control (ACC) vehicles using a constant spacing are investigated. Due to realistic design and execution, negative effect of tracking lag parameter on the stability is examined. An efficient analytical approach is presented in order to obtain a sufficient stability condition in the domain of the control parameters. The stability criterion is examined using a partial differential equation (PDE) approximation using large number of vehicles subjected to the time lags in vehicle dynamics and heterogeneity in the control laws, which allows asymmetry in the use of front and back information. The string stability analysis is performed to evaluate the disturbance attenuation. Finally, an example of multiple vehicle platoon control is presented, which demonstrates the effectiveness and the robustness of the proposed method.