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The uncomplicated answer is that there are names given for such differences and here they are.

The difference in distance divided by the difference in time is velocity.

The difference in velocity divided by the difference in time is acceleration.

The difference in acceleration divided by the difference in time is jerk.

The last term is somewhat informal, but not so uncommon, especially in engineering. The technical term jerk is sometimes manipulated to create humor because "jerk" is also the term applied to people who carry out senseless harmful acts, like the person who posted the original posting of an answer to this question.

Now, technically, to be correct, we have to point out that distance (or displacement) is a vector having magnitude and direction, so also is velocity and acceleration and hence so is "jerk" a vector. Also, technically, this discussion is all true in the limit of diminishingly small intervals of time and hence the correct representation of each of these divisions of differences is as a derivative, as one learns in calculus.

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Q: What do you get when you divide difference between acceleration by difference between time?
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