In this paper, we derive a vehicle-to-vehicle~(V2V) channel model assuming a typical propagation scenario in which the local scatterers move with random velocities in random directions. The complex channel gain of the proposed V2V channel model is provided. Subsequently, for different scatterer velocity distributions, the corresponding autocorrelation functions~(ACFs) are derived, illustrated, and compared with the classical ACF derived under the assumption of fixed scatterers. Furthermore, under specific conditions, highly accurate approximations for the ACFs are provided in closed form. Since the proposed V2V channel model covers several communication scenarios as special cases, including fixed-to-vehicle~(F2V) and fixed-to-fixed~(F2F) scenarios in the presence of both fixed and moving scatterers, it is obvious that the presented results are important for the designers of cutting-edge vehicular communication systems.