"In physics, acceleration is either speeding up or slowing down
depending on whether its sign is the same or opposite the sign of
velocity."
And John D. talks about it being inappropriate to discuss positive and
negative with respect to two or three dimensional vectors.
In my original post I stated I was talking about 1-D motion, which I
thought (maybe erroneously so) was what we were all talking about. I
assume this came up because at this time of year many HS and college
physics classes are studying velocity and acceleration in one-dimension,
and treating them as scalars.
If we have already moved to two or three dimensions and are now talking
about velocity and acceleration as vectors, then I gladly admit that my
same-sign/opposite-sign statement, as stated is not correct. I did not
think we were at the point of teaching about v and a as vectors.
On the other hand, it can still be considered correct in two or three
dimensions if we segment our discussion in terms of x velocity and x
acceleration... and y velocity and y acceleration... and z velocity and
z acceleration.
If the x-component of the acceleration is the same sign of the
x-component of the velocity, then the magnitude of the x-velocity will
be increasing. If opposite signs, then the magnitude of x-velocity is
decreasing. And likewise for y and likewise for z. Furthermore, the
velocity magnitude in one direction can be increasing at the same time
it is decreasing in another direction and at the same time it is staying
constant in the third dimension.
I think many students find it worthwhile to picture it this way... For
example in projectile motion in which the y-velocity decreases in
magnitude to zero, then increases in magnitude but in the opposite
direction... while at the same time the x-velocity remains constant.
Thus while I agree about the inappropriateness of positive/negative with
respect to vectors, it is not inappropriate with respect to the
components of vectors. It still seems to me that it is worthwhile to
envision whether a particular component of a velocity vector is
increasing or decreasing in magnitude, and this can be ascertained from
whether the sign of the velocity component and the sign of the
acceleration component are the same or opposite.
Of course this also can get us into the argument about what is part of
the "component." Is the minus sign in -3i part of the 3 or part of the
I or neither? Is it (-3)i or 3(-i) or -(3i)?
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu