Re: speed and velocity

[Mervin Koehlinger <tchkoehlimw@CRF.CUIS.EDU>]

On Tue, 24 Nov 1998, H. Scott Wiley wrote:

> 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).

I agree.  Average speed is simply the ratio of the total distance and the
elapsed time.  Average velocity is the ratio of the displacement and the
elapsed time.  The distance and the magnitude of the displacement may not
be the same for a particular motion.

>      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.

You are correct.  I continually emphasize with students that "+" and "-"
can only be used with vectors for 1-D situations (or for components in
multi-D situations) and that they refer to direction along an arbitrarily
chosen coordinate axis and nothing more.  The signs are just a convenient
shorthand for up/down, left/right, forward/backward.

Mervin Koehlinger
Physics Instructor
Concordia Lutheran High School
Fort Wayne, Indiana