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Obtaining a realistic and accurate model of the longitudinal dynamics is key for a good speed control of a self-driving car. It is also useful to simulate the longitudinal behavior of the vehicle with high fidelity. In this paper, a straightforward and generic method for obtaining the friction, braking and propulsion forces as a function of speed, throttle input and brake input is proposed. Experimental data is recorded during tests over the full speed range to estimate the forces, to which the corresponding curves are adjusted. A simple and direct balance of forces in the direction tangent to the ground is used to obtain an estimation of the real forces involved. Then a model composed of approximate spline curves that fit the results is proposed. Using splines to model the dynamic response has the advantage of being quick and accurate, avoiding the complexity of parameter identification and tuning of non-linear responses embedding the internal functionalities of the car, like ABS or regenerative brake. This methodology has been applied to LS2N's electric Renault Zoe but can be applied to any other electric car. As shown in the experimental section, a comparison between the estimated acceleration of the car using the model and the real one over a wide range of speeds along a trip of about $10km/h$ reveals only $0.35m/s^2$ of error standard deviation in a range of $\pm{2}m/s^2$ which is very encouraging.