Re: kinematics language

[Joseph Bellina <jbellina@SAINTMARYS.EDU>]

I'm not even sure I would say the y-velocity decreases...it gets less
positive, only the magnitude of the y-velocity decreases, and then of
course increases on the way down.  The y-velocity gets less positive
(assuming up is positive) the whole time, which is consistent with the
downward acceleration the whole time.

Much of this hinges on the distinction between something, as in the
value of the y-velocity, and how that quantity is changing.  This is not
an easy distinction for students, so any language that can add clarity
about this as well as the vector nature is valuable.

joe

On Wed, 28 Aug 2002,
Aaron Titus wrote:

> > >  >  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.
>
> Ugh, I did it again!  See how hard it is to be consistent?  You are
> right, it is improper to say that velocity decreases; it is proper to
> say the y-velocity decreases (in this case because the +y axis is
> defined to be upward).
>
> In fact, we will often find "velocity vs. time" graphs in our
> textbooks.  Even the RealTime Physics materials use velocity vs. time
> graphs (including the FMCE test).  But how can a vector be plotted on
> a graph as a function of time?  Obviously, the authors usually mean
> the velocity component such as v_x or v_y.  But why don't they just
> use the velocity component when plotting the graph if that's what
> they mean?
>
> I first noticed the inconsistencies when a student looked at a 2-D
> vector and asked, "Is that vector positive or negative?"  Now, I
> teach 2-D kinematics first.  Thus, students are always drawing graphs
> like v_x vs. t and v_y vs. t (or x vs. t and y vs. t, etc.).  On the
> occasion that the particular motion is 1-D, they still have to draw
> graphs for both components.  It helps to emphasize that we are
> working with vector components.  After trying this approach last
> semester for the first time, I noticed that there was less confusion
> with the vector nature of kinematics quantities.
>
> AT

Joseph J. Bellina, Jr.               574-284-4662
Associate Professor of Physics
Saint Mary's College
Notre Dame, IN 46556