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speed and velocity



In yesterday's interesting discussion on differences between proportional,
linear and affine, Sam Held made reference to velocity and speed
"However, I can see people using them interchanging them like velocity and
speed."

It seems to me that indiscriminate use of these two terms is a source of
confusion to students.
There are two avenues of confusion. Both derive from our tendency to use
the term velocity when we really mean (1) "magnitude of velocity" or (2)
"component of velocity".

(1) 'Speed" is a handy word for "magnitude of velocity". In most
applications outside the controlled conditions of the laboratory, it's speed
rather than velocity that is constant. In many introductory classes we
eschew the use of "speed" until we come upon uniform circular motion, where
we suddenly find it useful again. As long as we don't refer to "constant
velocity" when we mean "constant magnitude of velocity" or "constant speed",
I guess it's okay. My suspicion is that many of us fail on this count.

(2) This is the more serious problem. So much introductory kinematics is
based on the very artificial one-dimensional situation, In this context we
(and text-books) start talking and writing about positive and negative
velocities where what we mean are velocity components, (themselves scalar
quantities, like speed) along that special direction that we're pretending
all the action occurs. When a few lessons (chapter)s) later we move to two
and three dimensional motion, the students find out again that velocities
have directions, rather than signs!

I don't know of research directly on the question of how much lasting
confusing this indiscriminant use of the term velocity causes. Does anyone
out there?

With acceleration, there is no analogous term to "speed". Again, there is
plenty of opportunity to talk of "constant acceleration" when we mean
"constant magnitude of acceleration". Where lots of confusion and
contradiction can occur is in the use of the term "de-acceleration". In the
real 3-dimensional word, this means an acceleration that results in a
reduction of speed; in the artificial 1-dimensional world does
de-acceleration means "negative acceleration" or reduction of the velocity
component. Again, maybe a field worth some research or has that been done
already?

Brian McInnes