In a Vehicular Ad Hoc Network (VANET), the wireless Collision Avoidance (CA) system issues warnings to drivers before they reach a potentially dangerous zone on the road. This paper proposes an analytical model for evaluating the performance of emergency messaging via wireless CA systems. First, we utilize the dichotomized headway model, the braking model, and Greenberg's logarithmic model to generate vehicular mobility traces for analysis. Second, we derive the probability of a rear-end collision between two vehicles that travel in the same direction when a sudden event occurs. Third, we quantify the probability of vehicles failing to receive the emergency message. Numerical results from the model show that the number of car crashes per accident is much higher when a wireless CA system is not used. We also find it interesting that the number of car crashes is not directly proportional to the vehicle density when the vehicular mobility traces follow the speed-density relationship offered by Greenberg's logarithmic model. By integrating flow theory into VANET analysis, our model provides useful insights for future intelligent transportation.