We have numerically solved the equation of motion for a single vortex in a resistively shunted Josephson junction array. The vortex velocity (v), the damping coefficient and the dynamical barrier for the cell-to-cell vortex motion are studied. In particular, we have focused our attention on their dependence on the bias current , the penetration depth of the magnetic field , the vortex position (x), and the extension. The results obtained can be described in terms of the motion of a particle subjected to a potential , the analytical form of which is discussed as a function of the array parameters. Under certain circumstances, the injection of one vortex into the array may unleash a recursive process of vortex/antivortex creation that extends to the whole array. This gives rise to the formation of a stable dynamical state: the AVM (alternate-vortex motion), where vortices and antivortices move along alternate rows of plaquettes.