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Re: displacement and graphs



A little sidetrack here:

I've always had troubles at the beginning of intro courses trying to keep my
nomenclature consistent. The problem as I see it is as follows:

1) We usually start out defining velocity as the (change in
position)/(change in time).

2) The change in position can be considered a vector--the displacement--so
we can also say that the velocity is the displacement/(change in time).

3) However, we can also express any position as a displacement vector
(relative to some origin) and therefore the change in position is equivalent
to a change in displacement. Hence we can say that velocity is the (change
in displacement)/(change in time). In a calc course we will end up with v =
ds/dt.

4) Of course (3) is consistent with (2) since the change in displacement is
indeed another displacement vector. This is really no different then our
definition of acceleratiion as (change in velocity)/(change in time) since
the change in velocity is indeed another velocity--but we don't tend to talk
that way.

5) So--(change in position)/(change in time); displacement/(change in
time), (change in diplacement)/(change in time) are all equivalent---but I
suspect confusing to students. It is difficult to stay with just one of
these however when working through various examples.

fwiw

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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