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Re: speed and velocity



I think the problem is that vectors are not our natural language...not
surprising they are relatively recent things, even on the scale of social
evolution. Words like greater than or less than are about the size of
things, and so to me only confuse the conversation when you are talking
about vectors or vector components. Words like more positive or less
positive might be more appropriate, even though they sound unfamiliar.

I suppose another way of saying this is that we are intuitively polar,
and the polar language doesn't map well onto a Cartesian representation.


All of this just highlights how difficult the concepts of vector velocity
and vector acceleration are for students to internalizeOn Tue, 24 Nov 1998, H. Scott Wiley wrote:


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