Re: kinematics language

[Aaron Titus <titus@MAILAPS.ORG>]

> >  >  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