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They have this for the distance traveled with acceleration formula:

d= v*t + 1/2a*t^2

Now, I'm quite familiar with 1/2at^2 part, it's the v*t part that's troubling me.

If I have something going 1000m/s, and a deceleration of 10, for 50s, how far does it go?

According to the first forumla, it's

Code:

```
d = 1000 * 50 + .5 * -10 * 50^2
= 50000 - 12500
= 37500m
```

Ok, that's all well and good.

However, in a simple simulation, where I have an object moving along, I create a negative acceleration vector, and I apply the vector each time blip, and I see, "experimentally" (I quote because it's software that I wrote rather than some mechanical test I measured), that the object slows down in just the 12500 space. The object speed had slowed appropriately, but the distance is only the second part of the formula.

To be fair, I've never really seen the v*t prefix to the formula before. I've always seen the 1/2at^2 part. I guess they always assumed the object was stopped, and never really talked about decelerating. Of course, it makes sense the the original velocity must be considered.

So, either my experiment is wrong, (my sim is wrong, always a possibility), or I'm just misunderstanding how it's applied. It's not that I don't doubt my sim (bad information properly applied is still wrong), but the numbers work out using other formulas when cross checking. So, befuddlement ensues.

(Is there a better way to do math here, or do we just wing it?)