matrix notations for mathematical modelling

A car parked at point O is to be driven in a straight-line way from that point. Suppose that the distance of the car from O at time t is denoted by d(t) and the car is approached by a unit point mass that can be accelerated by using throttle and decelerated by using the brake. Let α and β denote the throttle acceleration and the braking deceleration respectively. Using appropriate matrix notations derive the state equations and hence the mathematical model of the process in the form.

Answer 1

[Walter Roberson]

If you put on the brakes when the car is stopped, the car does not go backwards, right? That implies that braking cannot be modeled as subtracting from acceleration. You will need to devise a consistent model for braking. Is braking more efficient or less efficient or the same efficiency at high velocities? What happens if you are using the throttle and the brake at the same time?

[Sean de Wolski]

Does abs braking kick in? What about the brakes heating up and being less effective once heated?