motor controller velocity profile (easeInOutCubic)

Maybe some can give me a nudge in the right direction:

I am writing a motor controller (will be in C/Wiring but modeling it in Actionscript). To avoid "jerking" when the motor starts and stops I want to ramp the motor speed. The standard way of doing this is through a trapezoidal velocity profile: constant acceleration by fixed amount at beginning + end of move. i.e.:

/ \

This works fine but gives a rather "flat" motion profile and I am trying to use Penner's 'easeInOutCubic' function instead.

Ok - here's the question (if you have read this far...;-):
I need to map the distance-based acceleration that the function yields to values for controlling the motor speed so I can ramp up/down the motor speed based on the distance to be traveled.

The motor is being PWM with a start speed of 60 and a max speed of 255 - so I need to ramp proportionally from 60 > 255 and back down to 60 over an arbitrary distance.

Seems like it is a simple math problem since I know the acceleration- ut I am having trouble getting my brain around it. Code below.



//this is AS 2- 
function easeInOutCubic(t, b, c, d) {
  if ((t /= d/2)<1) {
     return c/2*Math.pow(t, 3)+b;
 return c/2*(Math.pow(t-2, 3)+2)+b;
ball_mc = this.createEmptyMovieClip("ball", this.getNextHighestDepth());
ball_mc.moveTo(0, 0);
ball_mc.lineStyle(8, 0x000000);
ball_mc.lineTo(50, 0);
ball_mc.lineTo(50, 50);
ball_mc.lineTo(0, 50);
ball_mc.lineTo(0, 0);
 ball_mc._y = 100;
ball_mc.time     = 0; //time
ball_mc.begin    = ball_mc._x; //begin
ball_mc.change   =  Stage.width - (ball_mc.begin + ball_mc._width); //change
ball_mc.duration = 20; //duration   = true;
ball_mc.lastX    = ball_mc.begin;
ball_mc.onEnterFrame = function() {
   if ( {
         xPos = easeInOutCubic(ball_mc.time++, this.begin, this.change, this.duration);
         acceleration =xPos-this.lastX;
         this.lastX = xPos;
         this._x = xPos;
         if (this.time >this.duration) { = false;