I’ve previously posted about calculating the velocity needed for a particle to reach a certain distance when Drag is taken into account

After days of research and revisiting calculus problems, I came up with the equation I was looking for, but unfortunately this equation only works for CONSTANT speed, and doesn’t quite trace the roblox particle well when it takes Acceleration into account.

Roblox uses this equation to get the ratio at a specific elapsed time that the particle’s initial velocity should be scaled by when there is Drag:

```
function ratio(t, d)
return 2^-dt
end
```

where t = elapsed time, d = drag

And one can draw the path the particle should rise in (disregarding any vector values and only using scalar) with this following equation:

`f(x) = 1/2 * a * x^2`

where f(x) is the velocity/distance at the specific time, given “a” which is the scalar acceleration value.

How does roblox combine those two functions to simulate the path their particles travel in for Acceleration when there’s Drag?

I tried to multiply `f(x)`

by `r(x)`

which should calculate the velocity over time, and with a part, you can offset it’s current position by that value to trace the Particle, but the paths don’t seem to match at all.