You are in charge of programming the necessary braking to be applied in the event that the car's on-board compute

Context

You work with the team in charge of the automatic driving program at Tesla. You are in charge of programming the necessary braking to be applied in the event that the car's on-board computer detects a stationary obstacle that appears directly in front of the car.

Constraints

In order not to rush the passengers of the car too much, the program would like to brake as gently as possible.

To keep a certain safety margin, the program must stop 1 meter before reaching the obstacle.

Modelization

Start by modeling the acceleration required to bring the car to a complete stop (while respecting the constraints) as a function of the speed at which the car was initially traveling and the distance at which the obstacle appeared.

Then test your model by calculating the modulus of the acceleration needed for the following values

The car was traveling at 45 km/h;

The obstacle appeared 23 meters in front of the car;