Assuming one dimension for simplicity, the sign of velocity can be
positive or negative. Likewise, the sign of acceleration can be
positive or negative. This gives us four possibilities (not counting
zeroes) for the pairing of the signs of velocity and acceleration.
If the signs are the same (both positive or both negative) then the
object is speeding up... that is, the magnitude of the velocity is
increasing.
If the signs are opposite (one positive and one negative) then the
object is slowing down... that is, the magnitude of the velocity is
decreasing.
If students can feel good about this, then I feel I have made great
progress. In addition, I recommend that they not use the word
deceleration in physics class, even though most would assume that means
slowing down. The problem is that in common non-science usage,
acceleration means speeding up, and deceleration means slowing down, but
in physics acceleration does not mean speeding up... in half the
pairings of +/- velocity and +/- acceleration, acceleration means
slowing down. So it is best not to use deceleration/acceleration in
physics. It might be okay to say that deceleration always means slowing
down, but it is not okay to say acceleration always means speeding up,
therefore let's not use the deceleration/acceleration pairing the way
the general public uses them.
Likewise, it is not correct to associate negative acceleration with
slowing down, because if we take random pairings of the signs of
velocity and acceleration, in half of the cases of negative acceleration
the object is speeding up, and in half of the cases where there is
positive acceleration, the object is slowing down.
So I recommend staying with speeding up or slowing down rather than
signifying this concept with acceleration and deceleration.
Also note that in those cases for which the signs of velocity and
acceleration are opposite, if this continues long enough, they will
switch to the same sign. The best example is throwing an object
straight up. On its way up, the velocity is positive (assuming up is
positive) and acceleration is negative. With opposite signs, the object
is slowing down. Eventually the velocity reaches and passes through
zero and becomes negative. At this point the velocity and acceleration
are both negative, and the object speeds up until it hits the ground.
The physics in the previous paragraph is sometimes tough for students,
but it becomes much easier if they reach the point of understanding that
like signs for velocity and acceleration means speeding up, and opposite
signs means slowing down.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu