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First of all, learn about datatypes (right-click, representation).
Number of samples is an integer (I32), so change the representation. Should be blue.
"v" is a floating point number, not limited to integers, so that needs to be DBL Should be orange.
You can set dt=1 and worry about units later. (All unit scaling can be incorproated into alpha).
Alpha does not change during execution of the loop, so that terminal belongs before the loop.
Have you found the "add", "multiply", "x²", etc. They are all in the numeric palette.
So you get v(n-1) from the shift register, alpha and g from their terminals or constants, and wired all up, you get v(n), which you wire into the shift register on the right, and which will turn into v(n-1) on the next iteration.
Seems simple enough, right? Have you done any basic LabVIEW tutorials?
The calculation does not depend on [i], so don't wire anything to the iteration terminal. Adding [i] to dt makes no sense whatsoever.
The shift register only outputs the "v" value from the last iteration. To get all values, you need to autoindex at the loop boundary. (I would autoindex the value coming out of the left shift register, so the data starts with zero).
You can set dt=0.001 for the x-scale property of the graph.
Do you know how the graph for the velocity should look like? It should asymptotically reach terminal velocity right?