Re: [Phys-l] Deceleration or Negative Acceleration

["John Clement" <clement@hal-pc.org>]

Of course there is nothing wrong with + and - in the 1D situation.  There is
the question as to what is the best way to proceed.  Should one start with
2D or 1D?  The only book that I have ever seen that makes this clear is the
HS text, Minds on Physics, where they define + and - in the 1D situation as
being direction indicators, and they are very consistent with the notation.
This text would also be appropriate for a non calculus college course.

I recall there is some research that shows that students poorly link the 1D
and 2-3D examples.  They treat them as completely separate things.  There is
math research that shows the same thing with respect to volume and area.
One of the McDermott papers may have shown this problem.

Unfortunately things like the Real Time labs are heavily into 1D motion, but
they do ask the appropriate questions to help students clearly understand
the connection between signs, directions, and slowing down or speeding up.

John M. Clement
Houston, TX

> John M. disagreed with my statement...
>
> "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
>
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