Help with a movement formula

Hey, for a spell that I'm making the last days I got struck to find a correct formula for moving. What I want is this:
I have a unit with a speed of 15 units / 0.04 seconds (when this certain movement starts). The unit must reach a distance of 100 units in 0.4 seconds. That means that I got 10 intervals in which I have to multiply my speed with a certain acceleration to lower it in an constant way, so that my dummy will have reached the location in 0.4 seconds!

I tried using the standard physic movement formulas but failed, probably because I don't really know where to put the 10 intervals in which I multiply the speed with a one factor. 10 Intervals because the targeted location should be reached in 0.4 seconds with a period timer of 0,04 seconds.

Through testing I got to a factor of 0.96 which is very close to the "perfect" value. I almost get a distance of 100 units with it. But I want a formula because I like to have as many parameters of the spell to be customizable, just as as the speed factor. Thus I need a general formula.

I would be very, very thankful if someone could help me here. I tried physical movement formulas like 1 1/2 hours without getting a correct result

First: You should be subtracting a constant value from the knockback speed each update in order to properly simulate friction. Don't multiply.

Second: You're picking too many constraints for your knockback. The distance it covers and the time required to stop should be a natural result of the initial speed and the de-acceleration. Those are the only values you or your user need to customize.

This is no knockback. It's a spell with a location. And to reach that one I have to use fixed values. And I don't make something easy like the same speed or the same acceleration during the whole movement.

I guess you look for this formula

acceleration=(10/15)^(1/10)

Ahh looks like 0.96 was not almost perfect. Sorry.
And well with your formula I get 0,96. I also don't know why there isn't the max. distance parameter (in my case 100) involved.

Well I used an exponential function: y = b*a^x. Alright I admit I should have explained myself better... y is the distance you want to achieve (100 units / 0.4 seconds), b is the current speed (15 units / 0.04 seconds), a the unknown acceleration and x the intervals (10)

Now this formula is used: a = (y2/y1)^(1/(x2-x1))

If we set your x (10) as the x2 then x1 is 0 because we start at 0 intervals,

and your y (100 units / 0.4seconds) as the y2 then y1 is b (15 units / 0.04 seconds) because y1 is the b value at 0 intervals (x1).

Now just inserting a = ((100/0.4)/(15/0.04))^(1/(10-0)).


In my earlier formula in the (y2/y1) part I said 100/0.4 = 10/0.04 and then removed the two 0.04 divisions so I got 10/15...

Hmm but when I do this: 15 * 0.96 + 15 * 0.96^2 + 15 * 0.96^3 .... + 15*0.96^10 the result is : 120.832

If the thing is supposed to be slowing down due to friction with the ground, you're doing it wrong.

Try looking at my jump map, the code would be very similar. Found at http://www.wc3campaigns.net/showthread.php?t=81446.