Powertrain of an electric vehicle (EV) is a compound system with an electrical sub-system, such as batteries, inverters, and electrical motors, as well as a mechanical sub-system, including transmissions, differential, and wheels. Since the electrical systems directly affect the vehicle driving performance and dynamics of an EV, integrated modeling considering both the mechanical and electrical systems is essential to assess ultimate kinetic and dynamic characteristics of an EV in terms of input electrical quantities. In this paper, an entire analytic model for the powertrain of EVs is developed to describe EV dynamics with respect to electrical signals, in consideration of both mechanical and electrical systems. Theoretical models based on mathematical expressions, combining the mechanical power system and the electrical power systems, are derived for predicting the final vehicle driving performance as a function of electrical quantities. In addition, a Matlab model of an EV is developed to verify the derived mathematical analysis model. Based on the theoretical model of the powertrain, a variety of relationships between electrical quantities and vehicle dynamics, such as velocity, acceleration, and forces of the EVs, are finally investigated and analyzed.