Linear and exponential smoothing
The white circle is just the raw mouse movement. The blue circle is with linear smoothing, which means it goes at a fixed speed towards the mouse. The red circle is with exponential smoothing, which means it goes a fixed percentage of the way towards the mouse each frame. So the blue one just abruptly stops, and the red one slows down and stops.
The motion of the red one is a lot prettier, but nonetheless the math for it is also a lot simpler:
