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Re: speed and velocity



H. Scott Wiley wrote

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?


I agree this is a problem. It's one of the results of concentrating on
one-dimensional kinematics that I referred to in an earlier e-mail. (By the
way, it was good to read Bob Sciamanda's comments on this problem and his
description of his excellent approach to the problem.)
It's so easy to get the impression that velocity is something that is
intrinsically positive or negative and so a positive value, however small is
(algebraically) greater than a negative value! Scott's point about the
arbitrary nature of the choice of which direction is positive and which is
negative shows the absurdity of the algebraic approach. The use of the term
speed, rather than velocity, in the question can introduce some reality.
Brian McInnes