Feels like a good spot for some UI specialists to dig and to make some “vocabulary”. As you said a movement is a language. Something will move fast instantly and decelerate till zero if it moved from outside of the screen (accelerated in a virtual world outside of your “window”) or was bumped hard (but fasr acceleration is better in this case, as for me) because it was thrown by user to the “cart”.
IMHO for the “ to slide a text element in from the side” making ”decelerate X to 0” is always better. Question is “what’s X and is it quadratic or cubic” — that’s where we want to make some experiments. It comes from outside, so it moved at the moment we see it for the first time.
Maybe thinking in terms of using physical objects is the point.