Forty-eight years ago we invented another term you might
use for the time rate of increase of speed. We called it "fastering".
If there is some merit in introducing such a
quantity, pairing a different term with "speed", one might
use this term. Ultimately, of course, the physicist will
(or should) discard both concepts when teaching dynamics.
The origin of this strange term goes back to 1955, when I
took Physics 105 at Cal. We used "Principles of Mechanics"
by Synge & Griffith as our textbook. For reasons to which
we were not made privy, the authors eschewed the
conventional F = ma and wrote Newton's second law as
P = kmf ! You can readily see why we invented "fastering",
and P, of course, stands for "Phorce". The explicit k is
needed to accommodate pounds as mass units.