In my last posting, I noted that Lehrman and Swartz used "Graph of
displacement vs time" as the title for a graph of straight line motion:
They (L&S) go on to instantaneous speed v=limit (delta d)/(delta t) as
delta t ---->0. This is demonstrated to be the slope of a d vs. t graph
(labeled _displacement vs time_). According to my take on "cavalier" as
they use it, this is an example - offhandedly discarding the distinction
between position and displacement.
The use of "displacement" to label the axis of ordinates seems to have
popped up out of nowhere. At the very beginning of Chap. 3, they talk
about a position vs. time graph with the axes labeled "d" and "t."
However, they state that "d is used to represent its distance from the
origin." All their examples are consistent with d being a distance --
never negative. However (delta d) is described as a displacement as
previously mentioned, and it could be negative in the case of a downward
slope.
Having said this, I don't think it is bad to label the axis of ordinates
"displacement" if it fits in with the text. For straight-line motion, I
have always felt most comfortable with letting x be position (as on a
number line with positive, zero, and negative values.) When I taught
ninth grade algebra, this was part of the course. It was my experience
in teaching 12th grade physics that students liked to apply the ideas
that they learned in mathematics -- at the level of the texts by the
late Mary Dolciani, for example. They were always ready to use
"y=m*x+b," for example. (I recall that Clifford Swartz did not go along
with the "new math." I am not sure what "new math" is at the lower grade
levels, but I found that the pre-calculus mathematics books (I didn't
use the one by Dolciani until much later.) that correctly treated sets,
relations, functions, winding functions in trigonometry, and the
graphing of inequalities helped the students, and me, immensely. I
recall that parents used to call the school and ask if they were
teaching the "new math," as if it were a plague to be avoided. The
father of one student, a military officer, called me, intimating that I
wasn't teaching his son what was needed to do well on the College Board
math achievement exams. The other math teacher was very conservative and
traditional, favoring old-fashioned teaching materials. When the
College Board scores came in a few days later, all the students had at
least a 100 point gain over their scores the previous year with many or
most approaching 150 points gain. The student whose father called was
among those with a high gain over the previous year, and he was accepted
at West Point.) I think Clifford Swartz has much to offer in the
teaching of physics, but I do not go along with the apparent sloppiness
in mathematics.
In 1997-1998, I reviewed and corrected a number of errors, mostly
careless numerical errors, in fun@learning.physics. (I did not comment
on the author's use of the word "dynamics" as the study of motion.)
Although the author's web site seems to have disappeared, there is a
copy of the remnants of what is probably an older uncorrected version
at <http://www.scar.utoronto.ca/~pat/fun/fun/>. The once-nice JAVA
applets don't work well on my newer browser, and the links to the
author's page are now dysfunctional, but if one clicks on "Lessons" and
then "One-dimensional motion," one finds that the author, Dr. Mark
Sutherland, labels the axis of ordinates "displacement" rather than
"position" on an x vs. t graph. In the text, he explicitly calls x
"displacement." I suggested that he call x position and delta x
"displacement," etc. This was one suggestion he did not accept. I no
longer have his reply, but as I recall, he noted that if one parallel
transports a displacement (in two or higher dimensions), it is still
equal to the original displacement. If one translates a position vector,
the descriptor, "position," would not pertain to the same origin. If
forced to think about it, I always thought of a position vector as a
displacement from the origin, but it seemed inconvenient to think of a
displacement as a change of displacement, although that is what it
really is.