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Along with my previous efforts to decide how to write symbols for
kinematic parameters, I have also been struggling with how to deal
with 1D motion.
The book I am using (Serway) seems to really botch
things up. Basically, the whole chapter about 1D motion uses the
word "vector" when they usually actually mean "x-component of the
vector".
For example: " Average velocity can be either positive or negative."
" The average velocity is equal to the slope of the graph of position
vs time." " The graph of velocity vs time..."
The X-COMPONENT OF VELOCITY can be positive or negative. The
X-COMPONENT OF VELOCITY is the slope of x vs t. The X-COMPONENT OF
VELOCITY can be plotted on a graph.
Serway even admits that he botched the treatment of vectors in 1D
when he gets to the chapter on 2D: "This simple solution (using signs
to indicate direction) is no longer available in 2 or 3 dimensions.
Instead, we must make full use of the vector concept." In other
words, he didn't do things right the first time!
I expect that other books are similar.
How picky should we be? Is it so incorrect to say "plot v vs t" or
"velocity vs time" that it should be avoided? Even assuming that "v"
is the magnitude of velocity - rather than the true vector velocity -
is not right, because | v_vector | is always positive, but we are
perfectly comfortable plotting negative values on the graph.
Sticking to "v_x" or "x-component of velocity" the whole time would
seem to solve the problem without being too burdensome to either the
instructor or the students
I am currently planning: 1) to do vectors first from Ch 3 and discuss
components of vectors 2) to cover 1D motion from Ch 2, but be more
careful about the terminology 3) to finish Ch 3 and 2D motion.