Code:
if (KeyArray[sf::Key::W]) BallCoords.y -= SPEED * App.GetFrameTime();
I've gone through and started adding in things like this. I ran several tests for frame rate, both constrained by my monitor's refresh, and unrestrained. I've observed first hand now the impact changes in loop execution speed and frame-time delta can have on the physics.

Allright. Back to my laboratory. Thank you again VA, you're advice and instruction are valued.