When the engine gives a force of 500 N the car will reach a maximum velocity. Find what the value is

We consider here a simple model of the vehicle dynamics in Figure 1. The vehicle, of mass m, is acted on by a control force, u. The force u represents the force generated at the road/tire interface. For this simplified model we will assume that we can control this force directly and will neglect the dynamics of the powertrain, tires, etc., that go into generating the force. The resistive forces, bv, due to rolling resistance and wind drag, are assumed to vary linearly with the vehicle velocity, v, and act in the direction opposite the vehicle’s motion. The next step is to come up with some design criteria that the compensated system should achieve. When the engine gives a force of 500 N, the car will reach a maximum velocity. Find what the value is. An automobile should be able to accelerate up to that max speed in less than 5 seconds. In this application, a 10% overshoot and 2% steady-state error on the velocity are sufficient……………………. As reference if needed https://ctms.engin.umich.edu/CTMS/index.php?exampl… Requirements: 2 pages

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