Re: speed and velocity

["H. Scott Wiley" <hswiley@SWBELL.NET>]

Hi,

> ---Bob Sciamanda <trebor@VELOCITY.NET> wrote:
> > A serious problem arises when speaking of average speed.  The term
> > "average speed" can mean:
> >
> > 1) the average value of the magnitude of the velocity; or
> > 2) the total distance traveled divided by the total elapsed time.

I think the "serious" problem is extending the idea that speed is the
"magnitude of velocity" to "average speed is the magnitude of average
velocity."  This is wrong (in most cases).

While we're on the subject, can we really make comparisons of
velocities?  I posted the following on the ap-calc forum, but I'm still
not convinced that I'm wrong.  What do you think?

     Is it correct to say that a "velocity" of -4 m/s < +2 m/s ?
(and therefore that position increases when v>0, velocity increases when
a>0, etc.)  I have seen this suggested in several books, but I don't
agree.  The negative sign in the representation of a velocity vector
indicates the direction of the vector based on an arbitrarily chosen
system.  It is equally legitimate to assign down as + and up as -, as it
is to assign up as + and down as -.  When we compare two velocities or
decide when velocity is increasing or decreasing (a comparison), aren't
we really comparing "speeds"?  I try to stress this to my students, but
it is easy to fall back to the standard "calculus rules" when it comes
to determining maxima, inc/dec intervals, etc.  Am I wrong in my
thinking?  How do you approach this subject?  Do you use distance and
speed instead of displacement and velocity when comparisons are being
made?  What of acceleration and its derivative - the "jerk"?  Are there
corresponding scalar terms for these?

Thanks for your thoughts,

H. Scott Wiley
Weslaco High School
Weslaco, TX