Computational physics, programming in bash, linux.

Make a program that solves the following problem:

If two cars A and B move at the same constant speed of X m / s. The car A 10 meters behind B. The car B slows down speed at the rate of Y m / s ^ 2. Two seconds later the driver of the car A realizes the possible crash and steps on the brake, slowing down at rate 2 m / s^2.

The program must:

1. Calculate the value of the minimum acceleration a to avoid the shock 2. It will ask for the speed X and the decreased speed Y 3. Graph speed and position of cars (with gnu plot)