How to determine the error of ’dt in the stair step model when an object goes from 10 cm/s to 0 cm/s in 10 seconds

By: Zac Landis

First, to clarify what ’dt is, it is delta time or the change of time. The stair step model is when you have an object going at a linear velocity on a graph and trying to estimate the distance it goes.

Now to start off I used 1-second intervals, which means that in the 1^st second the object is going 10 cm/s, in the 2^nd second the object is going 9 cm/s, etc. That comes out to be that the object moves 55 cm.

Next, I used .5-second intervals, which means that in the 1^st .5 seconds the object is going 10 cm/s, in the 2^nd .5 seconds the object is going 9.5 cm/s. That is 52.5 cm.

After these two patterns were figured out I saw the possible formula, or equation, for this pattern and it is this, how far the object moves from its original position=’dt*5+50.

So, to make sure I was right I plugged in for .1-second intervals and got 50.5, but to check the formula I did it the way I had been. I still got 50.5.

Don’t mistake this as an absolute correct formula because I have yet to prove it

Z.L.