To understand the microscopic mechanism of nematic switching in many liquid crystal devices, we have performed a molecular-dynamics simulation study of the switching dynamics of nematics with positive polarizability anisotropy under an applied electrical field. Both pretilted nematics (PNs) and nonpretilted nematics (NPNs) under different field strengths are studied to investigate the effects of pretilt and field strength on the switching dynamics. Nematic molecules were modeled as rigid rods which experienced electrical torque, in a mean field approximation, imposed by uniform electrical fields. Our measured switching dynamics agree qualitatively with experiment by exhibiting initiation, fast reorientation, and slow relaxation stages. Coherence lengths under applied fields were estimated from the elastic constants calculated from our simulations. For all systems where the coherence length was larger than the simulation cell size (weak fields), unidirectional switching was observed. For field strengths yielding a coherence length smaller than the simulation cell size (strong fields), NPNs exhibited bidirectional switching. For the PNs, the reorientation of the global nematic director in response to the applied field was well described by a simple Leslie-Ericksen equation with the rate of reorientation being closely related to the torque due to the external field. For NPNs in the strong field regime, the local director within each unidirectionally switching domain exhibited reorientational dynamics similar to that of the PNs.