Simple mathematical model of a motor vehicle

Assume that a mathematical model for a motor vehicle is required, relating the accelerator pedal angle 6 to the forward speed u, a simple mathematical model might be 

Since u and 6 are functions of time, they are written u t) and 6 t). The constant a could be calculated if the following vehicle data for engine torque T, wheel traction force F, aerodynamic drag D were available  

Now aerodynamic drag D must equal traction force F 

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