Long Term Evolution (LTE) appears to be a practical and economical alternative to IEEE 802.11p for the rapid deployment of vehicular safety applications. Vehicles periodically broadcast messages, aka beacons, that contain their location and speed. Ideally, vehicles should have accurate knowledge of the locations of surrounding vehicles, and, if possible, have a same level of precision regardless of their speed.The contributions of this paper are twofold. First, we propose an efficient solution for adapting the generation rate of vehicles’ safety messages so that each of them experiences the same level of location precision. This fairness is attained using an analytical model, based on a queueing model that approximates the level of precision for each vehicle based on their motion speed and their generation rate of safety messages. Second, we present a solution for dynamically discovering the minimum number of resources, i.e. PRBs, that should be allocated by the LTE so as to meet a certain level of location precision for all vehicles. Our numerical results show the effectiveness of our two proposed solutions.