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Re: deceleration



Regarding John D.'s comments:

4) "Deceleration" is definitely an odd duck. The problem
is that students tend to assume that a deceleration must
be the opposite of an acceleration.

OK. Now I see your point.

According to that definition, a deceleration is a special
case of an acceleration. It is !!not!! the opposite of
an acceleration, just as dromedary is not the opposite of
camel. Half of all accelerations are decelerations.

This is a good example to use with the students when explaining
the definitions and the multiple meanings of the term 'acceleration'.

The puzzling thing is that AFAIK there isn't a Latin-based
word for the opposite of deceleration. If somebody can
find/invent one, please let me know!

Unfortunately, the appropriate Latin-based word *is* 'acceleration'
in its *vernacular* meaning. Here we have a case of physicists
taking a vernacular word and changing its normal meaning to be a
special technical vector derivative concept for their own peculiar
purposes. What would have been best is if *physicists* had used a
different term than 'acceleration' to mean the time rate of change
of the velocity vector. In that case the terms acceleration and
deceleration could keep their normal vernacular adversarial
relationship. But it's too late to fix that now, and I'm not about
to go on a crusade to get physicists to use a different term for
their derivative of a velocity vector. My point, though, is that
the reason for the confusion in the students' minds is the fault
of the physics community for having redefined a common term in a
way that is incompatible with its usual vernacular meaning.

But if speeding up results from a forward acceleration,
why not just use the obvious corresponding term "slowing
down" for the rearward acceleration? According to my
friends Strunk and White, if you want to communicate
parallel ideas, it is good style to use parallel words.

In that case it seems that we might be stuck with living with 2
common extant meanings for the word 'acceleration', one being the
everyday antonym of the everyday word 'deceleration', and the other
being the vector derivative of the velocity. As much as we may not
like it, the speeding up meaning of the term 'acceleration' is
already fixed in the population of English-speaking culture, and we
can't change that. In fact it's the prior ubiquity of this
'speeding up' meaning of the word (as well as its resistance to
change) that is a major cause of the problems students have
concerning the physics concept of acceleration as a vector
derivative.

Maybe the best we can do is to try to qualify our terms that have
multiple meanings with appropriate adjectival modifiers that
distinguish those meanings in various circumstances. For instance,
the terms 'component' and 'projection' in the context of vectors have
*both* a scalar meaning *and* a vector meaning. In this case I
recommend that we use the terms 'vector component', 'scalar
component', 'vector projection', and 'scalar projection' to properly
indicate which of the meanings that we have in mind at any given
time. Similarly, maybe we could allow the term 'acceleration' to
continue to have both meanings as long as we appropriately qualify
the term with an appropriate modifier so as to distinguish them in
any particular context. Maybe the phrases 'vector acceleration'
(for the time rate of change of the velocity vector) and 'scalar
acceleration' for a positive scalar derivative of the speed. In this
case the deceleration would numerically be the negative of the scalar
acceleration. Of course a potentially serious problem that could
develop from this dual use of the term acceleration with two
qualifying modifiers is from the observation that the scalar
magnitude of the vector acceleration is *not* in general the scalar
acceleration according to my suggested usage above. Another problem
is aesthetic. Appending the terms 'vector' and 'scalar' to the word
'acceleration' is not a very elegant solution to what is essentially
a vocabulary problem.

...
The most important point I'd like to make concerns _my_
speech not students' speech. I have a bad habit of using
"acceleration" and "deceleration" in ways that suggest
they are opposites.

This shows the strength of the ubiquity of the vernacular meaning of
the term 'acceleration'. This scalar meaning *is* part of the
language, and we aren't going to change it by our protestations to
the contrary.

Every time I do that I feel guilty,
because I feel I'm perpetuating a troublesome misconception.

I expect that you would only be actually guilty if you didn't
make clear at the time which meaning you had in mind when you
used the term. It seems to me that it is convenient to have a
word like 'acceleration' to mean the condition of speeding up,
just as it is convenient to have the word 'deceleration' to mean
the condition of slowing down. The big misconceptional problem
comes from an unwarranted mixing of the 2 main meanings of the
term 'acceleration' in the wrong context. I think the only way
to prevent the mix-up is to somehow emphatically indicate just
which meaning is meant at any given time. Using the term with
appropriate modifiers is not particularly elegant, but it might
work.

David Bowman

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.