Vehicles with adaptive cruise control (ACC) are an important component of smart and (semi-) autonomous roads and highway systems. These systems are envisaged to handle a large volume of manually driven and autonomous vehicles, ensuring smooth traffic flow. A reliable model capturing the dynamics of a vehicle is essential for developing techniques for model-based adaptive cruise control. The existing literature presents detailed models for individual subsystems are such as engine, brake, wheel etc. However, for analysing longitudinal motion, it is desirable to have a novel model capturing all aspects of the vehicle behaviour. In this work, we propose such a unified model of vehicle powertrain describing the dynamics of different components and interaction between them affecting the longitudinal motion. Lastly, using simulation studies, it is shown that the developed model can emulate the vehicle dynamics in the real-life scenarios such as maneuvering through congestion, stop and go, and sudden braking. © 2017 IEEE.