How do I make a video change positions smoothly?

I'm trying to figure out how to smoothly get a video clip in my project to move smoothly from one spot to another. I want it at first to speed up, but as it gets closer to its final position, to slow or ease into that position smoothly.

The only answer I've found online is to change the keyframes from "Linear" to "Smooth," but I notice no difference. It's still at the same constant speed. If there is a difference, how do I increase it?

Is there some sort of set way of doing this with keyframes, or is there a plugin I can use?