Just to get an estimate, what's "extremely fast"?
To due away with most "artifacts" you have to understand that your screen has only a fixed amount of pixels, so whenever you use a floating point position, OpenGL will have to estimate how to map the texture pixel to the screen pixel. Which can lead to issues where not the expected pixel gets used due to rounding up or down one pixel.
So to control the proper positioning, you can do the rounding yourself and match the pixels perfectly.
As for smooth movement you need to know that the frame time is not a fixed value. It varies slightly for every frame. As such the elapsed time isn't constant and thus your movement won't be constant.
For a "proper" physics calculation you should
Fix Your Timestep.