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One reason students have trouble with this idea -- that we are going to call it positive acceleration when a car that is moving backwards slows down -- is that they learn kinematics before they learn newton's laws. So without context, this seems like an intentionally baffling convention that we have chosen to inflict on them. I find it helps to give them a look ahead: I ask them to pretend that they are riding in a rocket sled on frictionless ice, only able to control their motion with two rockets: a forward rocket (actually located in back) and a retrorocket. I tell them that in physics, positive acceleration is what the forward rocket causes. Negative acceleration is what the retrorocket causes. I find this helps them to realize that either acceleration (+ or -) will sometimes involve moving faster, other times slower.
But I also find that this is one (of many) ways that my honors students separate themselves from my non-honors classes. In a non- honors class, I really have to ask myself is this issue worth fixating on? You can learn a lot of physics without leaving the one dimensional, one directional case. Even a simple freefall problem can be broken in two parts, treating up and down separately. It is not as elegant, but it avoids this issue and lets you move on. I am not a giant Hewitt fan, but I agree with him that kinematics can become a black hole...
-----Original Message-----_______________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of William Robertson
Sent: Tuesday, November 09, 2010 12:11 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] definitions ... purely operational, or not
I was a bit careless in my use of words. Specifically, I was talking
with this teacher about the use of kinematic equations in one
dimension. She was talking about (vf - vi)/t, in which although we do
use the term speed, because of the pluses and minuses involved in our
choice of what to put in for v, we are really dealing with direction
and therefore dealing with vectors. In such one dimensional problems,
you do have to choose a positive and negative direction. Which
direction is positive determines whether you assign and positive or
negative value to v. In this situation, stating that increases in
speed are always positive is a huge mistake. Suppose you assign plus
to the right and minus to the left. Then when something speeds up to
the right, you end up with a large positive v minus a smaller positive
v, and a positive acceleration. Fine. But if an object speeds up to
the left, you will end up with a negative rather than positive
acceleration, which is correct given your choice of plus and minus.
However, this teacher would be hamstrung by thinking that all
increases in speed are positive accelerations. So, I really was
talking about vectors, but was loose in my language.
As for accelerations and decelerations, you can talk all you want
about how these have been viewed historically and whether or not
someone is technically correct in their use, but we have to consider
the great confusion this causes with the average person trying to
understand science. While it might be correct to call slowing down a
deceleration, it is a short step for the learner (one the learner
often makes on his or her own) to deceleration being negative
acceleration. And of course what does one do with objects moving in a
circle? And "there is no such thing as deceleration" compares not at
all to "there is no such thing as centrifugal force." One is a choice
of words that makes things clearer (by they way, I do say that using
deceleration is fine in everyday language but confusing when dealing
with physics) and the other is a refusal to look at things from a
different frame of reference. Unless you want to say that rotating and
non-rotating frames of reference are like everyday language and
stricter language of physics.
At some point, we have to help people understand physics by using
consistent terms (I failed at that in my use of speed and velocity)
and not saying gosh, golly, gee it's okay for people to use different
language because well, you know, they're really not wrong historically
or some other way. What might be a minor difference in wording to a
physicist who can "get through" that to the heart of the matter,
becomes a major stumbling block for many.
Bill
William C. Robertson, Ph.D.
On Nov 9, 2010, at 12:25 AM, John Denker wrote:
On 11/08/2010 09:00 PM, William Robertson wrote:
Just this last week I was discussing with a group of teachers the
fact
that scientists consider all changes in velocity as accelerations,
and
that using deceleration might be lay talk, but not scientifically
appropriate.
Actually, if you listen to scientists, they use the term
"deceleration" all the time.
The trick is that there are two kinds of acceleration:
-- the scalar acceleration (d/dt) |v| == (d/dt) speed
-- the vector acceleration (d/dt) v == (d/dt) velocity
One teacher said that she accepted that, but that all
reductions in speed were to be considered negative accelerations and
all increases positive accelerations.
Note that she used the word "speed". In that context her
notion of acceleration and deceleration (aka positive and
negative acceleration) is formally and quantitatively correct.
A scalar acceleration is an increase in |v|.
A deceleration is a decrease in |v|.
In the short time we had, I
tried to help her understand that the world does not come with pluses
and minuses attached. She was the victim of previous educators who
deemed it "simpler" to assign increases in speed as positive and
decreases in speed as negative.
It's not just simpler; it's entirely true, so long as she is
using the word "speed". The speed is a scalar and therefore any
change in speed is either an increase or a decrease.
You can make the point that the laws of motion are much more simply
stated in terms of velocity rather than speed ... but you can't
say that speed is "wrong", and as long as speed exists then scalar
acceleration and deceleration will exist.
For thousands of years the word "acceleration" has meant an increase
in the scalar speed, and "deceleration" has meant the opposite, from
the Latin _celer_ = fast, swift, speedy. Physicists have extended
the word "acceleration" to apply to changes in the vector velocity
... and are in no position to complain when folks use the word in
its original sense.
It might have suited the purposes of
those educators at the time, but it blocked this teacher from
seeing a
bigger picture of how scientists analyze the physical world. That's a
case where educators used a technique that actually constrained this
teacher's understanding.
It's not that terrible. You just need to segue from the old scalar
acceleration to the new vector acceleration. It is not necessary or
even desirable to destroy the old notion. You just need to insist
that it is not what we want to talk about today. Today we want to
talk about motion in more than one dimension. The real world is
multi-
dimensional. In one dimension there is a notion of "increase" and
"decrease" but in higher dimensions there is not. That is to say,
quite formally, vectors are well-ordered in D=1 and not otherwise.
AFAICT her attachment to the term "deceleration" is symptomatic of
a much deeper problem, namely an attachment to a one-dimensional
model of kinematics. As always, fussing over terminology is not a
good idea. Ideas are primary; terminology is tertiary. Terminology
is important only insofar as it helps us formulate and communicate
the ideas. Once the multi-dimensional *concepts* are there, the
terminology will fall into place. If the concepts are not there,
then fussing over the terminology is 100% a waste of time.
=========
It is extremely common to find one word being used with two different
meanings. Sometimes this is no problem, because the proper meaning
can be figured out from context ... but sometimes it is a very serious
problem, especially when people don't realize the word has more than
one viable meaning. (This is an example where terminology hinders
rather than helps with the ideas.)
In thermodynamics, there are two inequivalent notions of "adiabatic"
and at least four inequivalent notions of "heat".
=========
I put "there's no such thing as deceleration" in the same category
as "there's no such thing as a centrifugal field".
-- It is entirely OK for the teacher to say we don't want to talk
about such things in this course.
-- It is not OK to say such things don't exist. They are perfectly
well-defined concepts, and they are /sometimes/ useful.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l