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



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