Vehicle road cooperation systems are the vital components of intelligent transportation systems, destined to play an irreplaceable role in the future smart cites. Such systems are mandated to achieve elevated data rates, ultralow latency, and enhanced reliability. To meet these requirements, we incorporate full-duplex (FD) and rate splitting multiple access (RSMA) into vehicle road cooperation systems and propose a downlink FD RSMA vehicle road cooperation system. More importantly, we introduce a crucial metric to evaluate the influence of the delay constraints on the system performance. Specifically, analytical expressions for the effective capacity of the nearby vehicle and the distant pedestrian are derived. We also provide the approximate expressions for the effective capacity at the low and high-signal-to-noise ratios (SNRs) and the upper bound on the effective capacity to gain further insights. Furthermore, we expand our evaluation to include both throughput and energy efficiency for the FD RSMA vehicle road cooperation system. Results illustrate that: the effective capacity of the nearby vehicle increases with the increasing transmitted power at low SNRs and stabilizes at a constant level at high SNRs. Conversely, the effective capacity of the distant pedestrian increases continuously with the higher transmitted power. The effective capacities of the vehicle and pedestrian are influenced by various factors, such as the transmitted power, power allocation coefficients, and Quality-of-Service exponent.