The proper performance of cooperative safety applications in vehicular networks depends of the exchange of beacon messages between neighboring vehicles. A challenge in these networks is to control the beacon transmission rate in real-time to meet the position accuracy requirements of safety applications. In this paper, we propose an adaptive beaconing algorithm based on dynamic control of beacon rate. The beacon rate is adjusted dynamically as a function of the vehicle movement status, to constrain the position error computed by surrounding vehicles. The results obtained from a realistic simulation framework show that, the proposed algorithm successfully controls the beacon rate to maintain a target position accuracy. Further, it adapts to the vehicular traffic dynamics, being able to maintain a better position accuracy compared to other fixed beaconing algorithms.