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Re: speed and velocity



John Mallinckrodt wrote


I think this is a little overly general. I agree with the concern
expressed about saying that -4 m/s is "less than" 2 m/s. But there are
plenty of times when the standard convention is exactly what we mean. An
altitude of -200 m *is* less than an altitude of +100 m; -20 degrees C
*is* less than +10 degrees C; etc.

Your examples are scalar quantities and the "standard convention" is
appropriate. The problem and ambiguity arises when we (and/or our students)
apply this "standard convention" to components of vectors such as velocity
or acceleration or force.

I like Tim Folkerts' suggestion of putting the sign with the unit vector
rather than the coefficient out front.

Ludwik's points out that "a v component is positive if an object moves along
the axis and
negative otherwise. But for accelerations it is "sometimes one way and
sometimes another", even in one dimension". Interpretations of acceleration
are not intuitive. Students need to think and talk through examples in word
form and then in graphical form before they achieve a real "ownership" of
the concept of acceleration. The published research of Lillian McDermott's
PER group and their presentation of appropriate curriculum material in
Physics by Inquiry show this well.

Brian McInnes