Re: kinematics language

["John S. Denker" <jsd@MONMOUTH.COM>]

Aaron Titus wrote:
> Recently I've been observing our use of certain words in teaching
> physics.  Some words are extremely confusing and I advocate not using
> them.  Other words, we often used inconsistently.

Right.  I would go even farther and say that the sloppy
words are only a symptom of deeper problems with wrong
physics.

> > The problem arrises when you want to talk about negative accelerations.
> > They are likely to see decceleration as a different conceptual thing,
> > rather than the negative, or opposite of acceleration. There will also be
> > a problem with negative velocities have positive accelerations.
>
> I suggest never using the word "deceleration".  If one means, slowing
> down, then I suggest saying "slowing down".

Slowing down means a decrease in _speed_, which is OK ... not to
be confused with a so-called "decrease in velocity", which is
an improper concept.

> If one means, an
> acceleration in the -x direction (or along whatever axis), then say
> that.

Right.

Properly speaking, "a quantity being negative" usually means the
quantity is less than zero.  Vectors can't be less than zero.  It's
just a wrong concept.  Non-wrong alternatives include the following:
 a) Perhaps some _component_ of the vector in this-or-that _basis_
    is less than zero -- but be careful, because such an assertion
    will be highly sensitive to the choice of basis.
    It is always possible and almost-always preferable to write
    the laws of physics in a form that is independent of the
    choice of basis.
 b) Better, the _projection_ of some physically-significant vector
    along the direction of some other physically-significant vector
    will turn out to be negative.  This can be expressed in terms of
    a dot product, without reference to anybody's chosen basis.

> If one means, an acceleration that is opposite to the
> velocity, then say that.

Yes, that would fit under case (b) above.

> >  They need to see that when a ball rises the velocity decreases at the
> > same rate that it increases as it falls, and conclude for themeselves in
> > the end that the acceleration is the same in both cases.

A velocity can't increase for the same reason a velocity
can't be negative.  Some _component_ of the velocity in
some arbitrarily-chosen _basis_ might be increasing, but
that is not the same thing.

> The words "increasing" and "decreasing" can be confusing if one isn't
> careful to distinguish between the magnitude of a quantity and the
> quantity.  I use this example in my class: If your checking account
> is in overdraft protection with a balance of -$400 and you deposit
> $300, has your balance increased or decreased? <increased>  Has "how
> much you owe the bank" increased or decreased? <decreased>

And that example is only in one dimension.  You can have an
ordering-relation in one dimension.  Students might be confused
about the relation, but at least it exists.  In higher dimensions,
no ordering-relation can possibly exist.

==========

I concur that it is probably best to avoid using the term
"deceleration" in physics class.  Acceleration is the
general term for a change in velocity, whether the
acceleration is
 -- in the same direction as the initial velocity (speeding up) or
 -- in the opposite direction to the initial velocity (slowing down) or
 -- perpendicular to the initial velocity (turning) or
 -- some combination thereof.

If I were forced to define deceleration, I would _not_
define it to be the negative of the acceleration. Instead
I would define it to denote exactly the same thing as
acceleration, but with the connotation that the acceleration
is directed more-or-less opposite to the initial velocity.