A lot of things *look* wrong to me in that code, but may not necessarily be wrong for what you're trying to do, so without making too many assumptions, I *think* that the *most likely* issue is that you should be using "partialTicks" where you're currently using "dt".
In fact, "dt" isn't even declared in the code you posted, so I can't say much about it (though I assume it stands for "delta ticks").
I'd try replacing "dt" with "partialTicks". If that doesn't do what you're looking for, try posting the full code so others can have a better understanding of how it's set up.
Edit 1 ======================================
I'm also pretty sure that this line:
this.particleX += vx;
should be in updateScreen, after the other 2 lines that are already there.
Edit 2 ===================================
Actually if you could post the full code that would be fantastic lol...I'd like to get a better idea of what's going on because otherwise I might be giving bad advice.