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The Continuously Variable Transmission (CVT) is a widely adopted transmission system. The operation of a CVT is simple, but successfully foretelling the longitudinal motion of a vehicle that utilizes this transmission is sophisticated. As a result, different vehicles taking part in BAJA-SAE competitions were developed using various strategies to model the vehicle’s longitudinal dynamics and CVT operation. This article aims to provide a tool for obtaining a quantitative estimate of the longitudinal performance of a CVT equipped vehicle and for the selection of an optimal drive-train gear ratio for such a vehicle. To this end, this article proposes a novel, relatively simple, and reasonably accurate mathematical approach for modeling the longitudinal motion of a vehicle utilizing a CVT, which was developed by a novel integration of existing vehicle dynamics concepts.