Safety and non-safety applications envisioned for Vehicular Ad hoc NETworks (VANETs) heavily rely on broadcasting for the exchange of data and status messages. New threats to road safety and efficiency raise if security requirements for broadcasting are not properly met. The decision whether or not a driver can trust information about a reported hazard should take into account the tradeoff between the decision delay, false warning probability and likelihood of missing the hazard. Although broadcasting in VANETs has been analytically studied at least for the simplified assumptions, related works do not jointly consider the reliability of the medium access control (MAC) protocol and the trust issues. In this letter, a new analytical model is designed for evaluating the latency required to guarantee trustworthiness in VANETs. This model explicitly accounts the operation of 802.11p/WAVE MAC protocol and computes mean decision delay as a function of number of vehicles, ratio of intruders as well as contention window sizes.