We propose an exponent-based partitioning broadcast protocol (EPBP) to promise the prompt dissemination of emergency message (EM) in vehicular networks. EPBP divides the communication range into segments with different widths iteratively. The width varies corresponding to the exponential curve. The design makes the farther no-empty segment thinner, as a result of which the collision rate of candidates' contention for the relay node decreases and the one-hop message progress increases efficiently. In addition, we adjust the interval of back-off timers to avoid the spurious forwarding problem, and develop more accurate analytical models for the performance. Our simulation verifies these models and show a significant increase of EPBP compared with the state-of-the-art protocols. EM dissemination speed can be improved as 55.94% faster in dense vehicle networks, and packet delivery ratio has risen to higher than 99.99%.