Re: speed and velocity

[Bob Sciamanda <trebor@VELOCITY.NET>]

-----Original Message-----
From: Brian McInnes <bmcinnes@PNC.COM.AU>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Monday, November 23, 1998 10:00 PM
Subject: speed and velocity
> . . .
> (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 ocities
> have directions, rather than signs!
> . . .

I have always avoided this problem by beginning the intro course with
vectors in 3 dimensions, including unit vectors, components, etc.  One
dimensional problems are then introduced as a special case involving only
one dimensional vectors (I still emphasize them as VECTORS).  The unit
vector can then always be canceled in any one dimensional vector
equation;  the direction of each term is then completely specified by its
sign.

To emphasize all this I explicitly write a unit vector with each term of
a one dimensional equation until it sinks in that it is superfluous
notation (but not a superfluous concept; we are still talking about
directed vectors). With care, one can in fact view the plus/minus signs
as one-dimensional unit vectors.

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor