So Let's say I have an object going at velocity $V$, initially. Each second, the current velocity $v$ is reduced by $v/x$ . After $250$ (arbitrary) seconds the velocity has been reduced to below/equal $0.01$ (arbitrary small amount). What is $x$?
The only formula I can really come up with describes only a single time-interval-step.
vnew = vold - (vold/x)
But I would like to have a formula where I can plug in:
-Initial velocity, Vinitial
-Number of time-steps, n
-Final velocity, Vfinal
...and get $x$.
(I hope this isn't too Physics-y for y'all. I'm not even sure if this can be done, but I thought that coming up with abstract formulas like this is more a mathematically-inclined thing so that's why I'm posting here.)
Assuming that you mean that each step down in speed happens exactly each second which is strange.
$$V_{n+1} = V_{n}(1-\frac{1}{x})$$
Therefore:
$$V_{n+k} = V_{n}(1-\frac{1}{x})^k$$
and
$$V_{f} = V_{i}(1-\frac{1}{x})^n$$