I think velocity etc. are derivatives of distance or displacement, not space.
And...please explain what is that jerk.

Jerk is the first derivative of acceleration, as acceleration is the first derivative of velocity.
It's important for large rockets whose thrust takes time to build.

I chose space over the words you prefer for its linkage to time in, e.g., space-time. In dimensional analysis, space, distance, displacement would all fall under the rubric length.

I think we cannot have velocities in mathematical spaces that are not metric; and the case that a metric measures distance or displacement is a shoe-in; so I must agree that "velocity etc. are derivatives of distance or displacement." I don't agree that "not space" follows, however.

Distance is measured between points in space or between points in a metric (mathematical) space.
It follows that space and distance are mutually dependent; so the metonymy that puts space for distance is natural, even though space has many other meanings (one of which is time: in the space of a few minutes).

"How long does it take to cross the space between the earth and the moon?" is a question about average speed, and does not differ in meaning from "How long does it take to cover the distance from the earth to the moon?"

Which is not to say your physics students ought to copy my language; and my example may be said to be drawn from the vernacular, not the scientific register.

Another thought occurs. In both a Euclidean and a hyperbolic space, when we speak of velocity, we mean distance over time; but what we mean by distance is--in a certain way--different. The objection to space is its imprecision, but its very imprecision reflects a greater generality.

You see your comment has been stimulating.

I'm reminded of "Every language has a design," Eldad's translation from the Portuguese. An excellent translation; but fault may be found with the original: Esperanto was designed, Hebrew not.

I suppose we can agree that not all sentences are created equal.

Oh, what an accelerated response!
Thank you (:
And, of course, I revised the Hebrew translation.

Having had some time to think, I have decided to stick with my original sentence for the reasons I have given. But for your excellent reason, I have added an English translation that substitutes distance for space: better for translators and better for physicists. The original _may_ be better for poets.

...and better for engineers like myself.