Emerging 802.11p vehicle-to-vehicle (V2V) networks rely on periodic Basic Safety Messages (BSMs) to disseminate time-sensitive safety-critical information, such as vehicle position, speed, and heading -- that enables several safety applications and has the potential to improve on-road safety. Due to mobility, lack of global-knowledge and limited communication resources, designing an optimal BSM broadcast rate-control protocol is challenging. Recently, minimizing Age of Information (AoI) has gained momentum in designing BSM broadcast rate-control protocols. In this paper, we show that minimizing AoI solely does not always improve the safety of V2V networks. Specifically, we propose a novel metric, termed Trackability-aware Age of Information TAoI, that in addition to AoI, takes into account the self risk assessment of vehicles, quantified in terms of self tracking error (self-TE) -- which provides an indication of collision risk posed by the vehicle. Self-TE is defined as the difference between the actual location of a certain vehicle and its self-estimated location. Our extensive experiments, based on realistic SUMO traffic traces on top of ns-3 simulator, demonstrate that TAoI based rate-protocol significantly outperforms baseline AoI based rate protocol and default $10$ Hz broadcast rate in terms of safety performance, i.e., collision risk, in all considered V2V settings.