Re: [Phys-l] definitions ... purely operational, or not

[William Robertson <wrobert9@ix.netcom.com>]

Works for me, but I think students truly understand the concept(s)  
when you describe the situation and then let them assign positive and  
negative directions and figure out, from the definitions of velocity  
and acceleration, what's going on. When they can work from first  
principles, you know they get it.

Bill


William C. Robertson, Ph.D.


On Nov 9, 2010, at 12:01 PM, Michael Edmiston wrote:

> When studying motion in one-dimension, and assuming positive velocity
> indicates motion in one of the two available directions and negative
> velocity indicates moving in the opposite direction, then I have been
> reasonably successful using the following train of thought with my  
> students.
>
> * * * *
>
> (1) Velocity will have a positive or negative sign indicating the  
> direction.
>
> (2) Acceleration will have a positive or negative sign as calculated  
> from a
> = (vf-vi)/t.
>
> (3) If the signs of the velocity and acceleration are the same (both
> positive or both negative) then the speed of the object is  
> increasing, and
> in everyday language we say the object is accelerating.
>
> (4) If the signs of the velocity and acceleration are different
> (positive/negative or negative/positive) then the speed of the  
> object is
> decreasing and in everyday language we say the object is decelerating.
>
> Also notice the following points...
>
> (5) Since negative acceleration will mean "speeding up" when the  
> velocity is
> negative, and since positive acceleration will mean "slowing down"  
> when the
> velocity is positive, it is not a good idea to associate positive
> acceleration with speeding up and negative acceleration with slowing  
> down.
> Doing so will make you wrong in 50% of the possible cases.
>
> (6) When the object is slowing down (opposite signs of acceleration  
> and
> velocity) it won't stay that way forever.  If the acceleration  
> continues at
> a nonzero value and keeps it's original +/- sign (originally  
> opposite the
> velocity), the initially slowing down object will eventually come to  
> rest
> then begin to speed up in the opposite direction of what it was  
> originally
> going.
>
> * * * *
>
> I don't like the forward rocket engine, reverse rocket engine analogy
> recently given.  If the rocket is moving forward and the reverse  
> engine is
> fired, the rocket initially slows down, but if the reverse engine  
> continues
> to fire, the rocket will slow to zero, and will then speed up in the  
> reverse
> direction.  We have the similar situation if the rocket is originally
> traveling "backwards" and the forward engine is fired.
>
> I don't think analogies work very well here if separated from the  
> arithmetic
> of viewing the signs of the velocity/acceleration as +/+ or -/-  
> (speeding
> up).... compared to... +/- or -/+ (slowing down)... and realizing  
> the +/-
> or -/+ situations cannot stay that way.
>
> Of course the (+/+) and (-/-) can't stay that way either, but that's  
> for a
> different reason... some limit to the top speed is eventually reached.
>
> Michael D. Edmiston, Ph.D.
> Professor of Chemistry and Physics
> Chair, Division of Natural and Applied Sciences
> Bluffton University
> 1 University Drive
> Bluffton, OH 45817
>
> 419.358.3270 (office)
> edmiston@bluffton.edu
>
>
>
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