We present a single lane car- following model of traffic flow which is inertial and free of collisions. It demonstrates observed features of traffic flow such as existence of three regimes: free, nonhomogeneous congested (NHC) or synchronized, and homogeneous congested (HC) or jammed flow; bistability of free and NHC flow states in a range of densities, hysteresis in transitions between these states; jumps in the density-flux plane in the NHC regime; gradual spatial transition from synchronized to free flow; long survival time of jams in the HC regime. The model predicts that in the NHC regime there exist many stable states with different wavelengths, and noise can cause transitions between them.