In this paper, we propose an analysis of broadcasting in the IEEE 802.11p MAC protocol. We consider multi-channel operation which is specifically designed for VANET (Vehicular Ad hoc Networks) applications. This protocol supports channel switching; the device alternates between the CCH (Control Channel) and the SCH (Service Channel) during the fixed synchronization interval. It helps vehicles with a single transceiver to access the CCH periodically during which time they acquire or broadcast safety-related messages. Confining the broadcasting opportunity to the deterministic CCH interval entails a non-typical approach to the analysis. Our analysis is carried out considering 1) the time dependency of the system behavior caused by the channel switching, 2) the mutual influence among the vehicles using a multi-dimensional stochastic process, and 3) the generation of messages distributed over the CCH interval. The proposed analysis enables the prediction of the successful delivery ratio and the delay of the broadcast messages. Furthermore, we propose a refinement of the analysis to take account of the effects of hidden nodes on the system performance. The simulation results show that the proposed analysis is quite accurate in describing both the delivery ratio and delay, as well as in reflecting the hidden node effects. The benefits derived from the distributed generation of traffic are also evidenced by the results of experiments.