Ok, ok I see what you're saying Error014. I don't understand even one of those equations ^^ but here's what I have based on what you've said here:

Initial speed is 10 q/s (quants per second)
Deceleration is 10% of the initial speed

the code decelerates like this:

move_speed -= (Initial speed* deceleration percent)*time_step;

So in other words:

move_speed would initially be 10 being decreased by initial speed* deceleration percentage

so the equation there would be:

move_speed -= (10 * 0.1) *time_step;

all I need is to find out at what point it should start decelerating.