Creating a collumn based on a diffrent collumn with a formula applied

I think CRIMEDOG is close, but there are some tricks to this.

First, I understand you are new to Excel. It's a great tool. If you don't plan on using Excel again, then glad to help and you can move on. If, however, you expect to start using Excel more, then I strongly suggest you get a book or visit youtube for some Excel education. What you ask is very simple, but I understand it can be challenging when first working with excel.

Second, the way you have your data arranged, you can match 'i' in your equation to the row (the numbers you see going from 1 to 34 in your picture). I am unsure if x(i) is column B or column F - I am assuming B, so adjust if necessary.
Since your data starts on row 2, x(2) is value is 642 (cell B2), x(10) is 803 (cell B10). Similarly, your t values are in column A and your y values are in column C. Explaining a bit further, t(5)=1.6, x(5)=644, and y(5)=66 and correspond to cells A5, B5, and C5, respectively.

I am not sure what your dt is. I assume it is t(i)-t(i-1), but it could also be t(i+1)-t(i-1), or t(i+1)-t(i). You'll need to determine that based upon your formula.

So, for vx(i), you need to use the x value above that row, the x value below that row and then your delta t (dt). So, for example,
vx(3) = x(4)-x(2)/(2 * (t(i) - t(i-1)) =>
H3 = (B4 - B2)/(2 * (A3 - A2)) = (649 - 642)/(2 * (0.8 - 0.4))

You have derived the excel equation you need to put in H3 for your vx(i) equation. In H3 (or is it F3 in your table) type
=(B4 - B2)/(2 * (A3 - A2))
A great trick for excel is to now click on cell H3. There will be a rectangle around the cell and a little black box on the bottom right of the rectangle. Click on that box and drag it to the bottom of your data (e.g. H39). Excel will increment each of the numbers in your equation automatically. Again, this is the type of stuff you learn in the tutorials which will make excel that much more easy to use.

Boa sorte