An analytical model for an electric vehicle (EV) powertrain has been developed in this paper to study the vehicular dynamics, based on a Nissan Leaf EV. The electrical components of the powertrain include a battery pack, a battery management system (BMS), a DC/DC converter, a DC/AC inverter, a permanent magnet synchronous motor (PMSM), and a control system while the mechanical system consists of power transmissions, axial shaft and vehicle wheels. The driving performance of the EV is studied through the real-world driving tests and simulation tests in Matlab/Simulink. In the analytical model, the vehicular dynamics is evaluated against changes in the vehicle velocity and acceleration, state of charge (SOC) of the battery, and the motor output power. Finally, a number of EVs are introduced in the system to optimize the power dispatch. The greenhouse gas emissions of EVs are analyzed under various driving and charging conditions, and compared with conventional internal combustion engine (ICE) vehicles. For a given driving cycle, Nissan Leaf can reduce CO2 emissions by 70%, depending on its duty cycle and the way electricity is supplied.