Re: [Phys-l] Deceleration or Negative Acceleration

[Steve Highland <shighlan@uslink.net>]

> On 09/09/2008 07:02 AM, pschoch@nac.net wrote:
> > A student has asked which is
> > proper terminology: "Negative Acceleration" or "Deceleration".
 
I agree with everything you have to say below.  What I'm wondering about is
what is the best order in which to introduce these things to students?

We almost always start with one-dimensional motion, and that naturally leads
to the usage of +/- signs to represent directions but it also leads to the
wrong ideas that vector quantities can be positive and negative.

Is there any way to begin with the broader concept so the special case of
one dimension doesn't mislead so badly?  I remember Aaron Titus talking
about this years ago but I never really paid attention to where he went with
it after that.

Steve Highland


> As is so often the case when people are talking past each other,
> multiple different concepts are being mooshed together.  Today
> there are three cases to consider:
>  a) the _scalar_ acceleration associated with the (scalar) speed.
>  b) the _vector_ acceleration associated with the (vector) velocity
>    in one dimension.
>  c) the _vector_ acceleration associated with the (vector) velocity
>    in more than one dimension.
>
> In more detail:
>
>  a) It is perfectly reasonable to talk about speed. Speed is a
>   scalar. The derivative of speed is the _scalar_ acceleration.
>   The scalar acceleration can be positive or negative.
>   Deceleration is implicitly and intrinsically a scalar concept,
>   and corresponds to the negative of the scalar acceleration.
>
>   As we all know (but the students don't know, especially in
>   September), the laws of motion are most simply expressed in
>   terms of velocity, not speed. So we don't spend tons of time
>   talking about scalar acceleration and deceleration.  In any
>   case, the terms are perfectly well defined except as noted
>   below. They are often useful.
>
>   The scalar acceleration is what you get if you project the
>   scalar acceleration onto the direction of motion. It is
>   _undefined_ when the velocity is zero. It is badly behaved
>   in the limit as velocity goes to zero. (The limit does not
>   exist.)
>
>  b) There is no accepted definition of deceleration when applied
>   to vectors, even in one dimension.  It might be theoretically
>   possible to define such a thing, but it would be unhelpful
>   because it would not be consistent with the already-existing
>   meanings of the word.
>
>   Also: In one dimension, there is a one-to-one correspondence
>   between vectors and scalars.  This means we can talk about
>   "positive" and "negative".  However, this is usually not
>   a good idea, because ....
>
>  c) If/when we are talking about vectors in two or more dimensions,
>   there is no such thing as positive or negative.  By definition,
>   positive means >0, while negative means <0, and there are no <
>   or > operators in two or more dimensions.
>
>   Vectors have magnitude and direction.  You can talk about
>   leftward acceleration or rightward acceleration or forward
>   acceleration or rearward acceleration or anything in between,
>   but you cannot talk about positive or negative when you are
>   talking about vectors in two or more dimensions.
>
>
> =================
>
> To summarize:  Talking about scalar acceleration, negative scalar
> acceleration, and deceleration is perfectly correct.  It has
> little direct value in a physics class, but it ought to be
> mentioned, if only so that the students can acquire a clear
> concept map that _separates_ the older notion of scalar acceleration
> from the newer notion of vector acceleration.
>
> When talking about vector acceleration, any mention of positive
> or negative is improper.  Any notion of deceleration is improper.
>
> In physics class, if you mean scalar acceleration, say _scalar_
> acceleration;  in contrast, the unadorned term "acceleration" means
> vector acceleration, unless the context clearly requires otherwise.
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l