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A) In physics, we need a name for the quantity (dv/dt).
It's the same quantity that shows up as (F/m) in Newton's
second law. We like to use reference frames that lack
this quantity.
B) Alas, calling this quantity "acceleration" sometimes
causes problems for students. They think that acceleration
denotes an increase in speed, and that it is the opposite
of deceleration. This leads to wrong physics conceptions
in two ways:
-- Speed is a scalar, whereas velocity is a vector.
The quantity under discussion is a change in velocity,
and must not be confused with a change in speed.
-- We don't want two words (acceleration and deceleration)
when one word will do. A force in the forward direction
causes an increase in speed, while a force in the rearward
direction causes a decrease in speed, but we want to use
the same word to describe both of these cases (plus a
third case, namely sideways force).