This paper presents a mathematical model of an electric driveline consisting of one battery pack, two independent Permanent Magnet DC (PMDC) motors and motor-controllers and two fixed-ratio planetary gearboxes, all located inside the rear frame of the vehicle.The proposed analysis has been performed with the objective of: (i) Determination of acceleration run time for a straight patch of 75 meters; (ii) Determination of lap times and energy consumption for endurance track of 23 laps. A model of a PMDC motor and motor controller has been developed based on response analysis by conducting experiments on a jig setup. The motor controllers are compared for two control modes- Speed mode and Torque mode. A simplified race car model for longitudinal vehicle dynamics is derived from forces acting on the car including the effect of losses due to drag forces, rolling resistance, transmission inefficiency and inertial losses due to rotary elements. The effect of reduction ratio on acceleration run times and endurance lap times and energy consumption is compared and an optimum gear ratio is finalized considering acceleration performance and mass and inertia of resulting gearbox. An estimate of maximum energy utilized during the endurance run is obtained based on motor current profile and speed-torque characteristics, and the battery pack size and configuration is decided accordingly. The cells for the battery pack have been selected after extensive market research based on constraints like energy requirement, weight and maintenance cost.This concludes the entire mathematical model for the driveline of the vehicle pertaining to the most optimized performance.