It really helps to put units everywhere, since thats an easy way to check the math. Aaron actually nailed it: Without units, all your values don't make any sense. Note please that since "quant" is defined as some kind of distance (in Acknex), you could actually say "the speed is 10 quants per second".


I'm not sure I totally understood your question. When you say "The deceleration of the object is 10% (0.1*10)", do you mean the deceleration has a constant value - say 0.1 m/s²? which would mean the deceleration is constant, or is it always one tenth of the current speed (which kind of messes up the units, but hey!)

I hate not using units, but whatever, we'll roll with it.

I'll just pretend the speed at the beginning is "v0 = 10", the decelaration is a=0.1 (see? I took the constant value, since thats so much easier).

If the objects starts decelerating, it will stop when the speed is zero, right? Makes sense. For a constant acceleration, you can get the speed at the time "t" with:

v(t) = v0 + a*t

obviously, since we're decelerating, "a" actually has a negative value. In order to continue with "a=0.1", we'll put the minus right there. From now on, always remember the directions! (velocity, accerlation, etc. are actually all vectors!). For our time t, the object needs to stop:

v0 - a*t = 0 <-> t = v0/a

The distance your object moved in a time t when it starts at 0, has the speed of v0 and decelerates with a (a>0) (and a is a constant value=, you can use this equation:

s = v0*t - 1/2 * a * t²

Since we already know our "t", and since we - in this case - got a simple expression for it, we can place it in there

s = v0²/a - 1/2 * v0²/a = 1/2 * v0²/a

thats "500" ( = 1/2 * 100/0.1 = 1/2*1000) in your "units".
Since we actually want to get to the point "1024", we need to start decelerating at

1024-500=524

At what time did it originally reach that place? Well, before decelerating, it was moving with the constant velocity "10", and there was no accerlation or deceleration. Therefore, we can say that it travelled the distance "s" in a time "T" (I'm now using a capital letter in order to avoid you being confused with the "t" we had before. Please note that you don't usually use a capital letter here (even though it really doesn't matter all that much ;)))

s = v0*T
<-> T = s/v0

since we want to travel 524 metres, we get

T = 524/10 = 52.4

So it needs to start decelerating at "52.4" (your units).

Also note that if we had palced units here, we would always get the correct unit (i.e. for the last one, we'd have calculated T = 524m/(10 m/s) = 52.4s)

Of course - this complete thing was mainly assumption on my part. I really don't know if I got your questions right, so don't hesitate to ask or elaborate.


Extra note: I'm tired as per usual, so there are likely dozens of mistakes in here. Whoops.