Acceleration, the right way?

Hey everyone,

I've been trying to create a new class of vehicle and simulate a somewhat realistic acceleration/velocity relationship and behavior but with no success.
At least, I can't figure out how to do what I want to do.

Which is this:
I have a vehicle with a maxVelocity and an initialAcceleration properties, and what I want to find out is how to express the vehicle's acceleration with the two above mentioned variables so that the vehicle stops accelerating when it reaches its maxVelocity (meaning that acceleration reaches 0).

I believe there are some serious maths going on behind this seemingly simple thing, at least too serious for me, and I tried to remember what I learned years ago about arithmetic progressions and stuff like that but to no result other than a headache.

Does someone know how to do it, if it's actually possible. And if not, how you guys do to simulate an acceleration that looks like a car's gear.

Thanks!

Here is a simple script how you can control the acceleration, no big math.

PHP Code:

---

import flash.utils.Timer;
import flash.events.TimerEvent;

var counter:int = 1;
var accValue:Number;
var myTimer:Timer = new Timer(1);
myTimer.start();
myTimer.addEventListener( TimerEvent.TIMER, cHandler);
function cHandler(event:TimerEvent):void
{
    counter++;
    accValue = counter * 0.01;
    if(accValue >= 2)
    {
        accValue = 2;
    }
    mc.x +=0.1 + accValue;
} 


---

Thanks for your answer cancerinform.
Actually, this is not what I need and I figured out how to just do that myself last night!
It was actually very very easy... I don't know why I kept thinking it was difficult so I kept looking into complicated formulas and stuff and got stuck. The answer is much simpler than that. Take a look:

Actionscript Code:

velocity += acceleration; //as usual, add the acceleration to the velocity

/*
* set the acceleration to be half
* (or third or whatever you need)
* of what is basically the remaining
* acceleration needed to reach maxVelocity
*/
acceleration += (maxVelocity - velocity) / 2;

/*
* zero out the acceleration when
* low enough since technically it'll never reach it
*/

if (acceleration < .1) acceleration = 0;

And that's it...! Sometimes, you need a good night of sleep to reboot your brain and basically stop looking for difficulty where there is no need for it :)