It is seems that what you need is not a real time simulation. You just need to show how displacement and velocity changed with time for constant acceleration.
The formula is all well know:
x(t)=x(0)+v(0)*t+0.5*t*t;
v(t)=v(0)+a*t;

Use the above equestion directly will be the easiest way to implement.
You can show the x-t or v-t diagram directly.