In the public vernacular, acceleration and deceleration apply to
instantaneous speed rather than velocity. Remember instantaneous speed
is the "magnitude" of velocity and is unsigned... there is no such
thing as negative instantaneous speed. In this manner of speaking,
acceleration means the speed is becoming a larger number, and
deceleration means the speed is becoming a smaller number.
In standard physics notation, and assuming one-dimension, a negative
velocity means the velocity points in the negative direction. Likewise
a negative acceleration points in the negative direction. Hence
negative acceleration coupled with negative velocity implies the
velocity increases in magnitude as the object travels in the negative
direction... that is, the object is speeding up.
Example, assume you're in a car. Forward is positive and backwards is
negative. Put the car in reverse and give it some gas. You get a
negative acceleration and a negative velocity. The popular description
would be you are accelerating (speeding up) in the backward direction.
The easy way to remember this is: (a) if the physics velocity and
acceleration have the same sign, we have the common definition of
acceleration (speeding up). (b) if the physics velocity and
acceleration have opposite signs, we have the common definition of
deceleration (slowing down).
Each year, some of my students tell me that they were taught, in high
school, that negative acceleration means deceleration. Of course I
don't believe everything my students tell me. But if this is true,
they were taught incorrectly. I asked my son about this (he is in HS
physics now). He is being taught correctly, but I'm glad I asked him
because he was a little confused about it... probably because he wasn't
paying as much attention as he should have been.
One more interesting point. If the acceleration is constant-sign for a
long time, then if the signs of acceleration and velocity are the same,
they will stay the same, and we keep speeding up. However, if the
acceleration is constant-sign for a long time, and the signs of
acceleration and velocity are opposite, they won't stay that way. We
decelerate (slow down) until we reach zero velocity; then we begin to
accelerate (speed up) in the direction opposite to which we started.
Some physicists object to letting the popular meanings of acceleration
and deceleration creep into formal physics. I do not object. I think
it is important for the students to make the connection between the
formal stuff and the everyday stuff. I think they're perfectly capable
of understanding that the word acceleration has slightly different
meaning in physics than in everyday life. If I can manage to get it
straight in a student's mind, it typically is an "aha" experience for
them and they won't forget it.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817