Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Symbols for Kinematics



Arnold Arons argues that kinematic equations should be written in terms
of time intervals, not clock readings (instantaneous values of time).
See, for example, Arons, Arnold B. (1997)
_Teaching_Introductory_Physics_, Part I, pp. 23-25.

Daniel Crowe
Loudoun Academy of Science
dan.crowe@loudoun.k12.va.us
FolkertsT@bartonccc.edu 08/09/07 11:18 PM >>>
As, I prepare for this coming year, I am trying to decide what symbols
to use for topics from kinematics (which will naturally extend through
much of the semester).

For simplicity, let's look at the equation relating velocity,
acceleration and time.
This equation is commonly written as

v = v_0 + at

but there are many possible variations. For example, instead of "t"
sometimes you see "delta(t)" or "t_f - t_i" or "t_f - t_0". Instead of
"v" you might see "v(t)" or "v_f". Or you might see velocities combined
as "v_f - v_i" or "delta(v)" on the left side.


ARE THERE PEDAGOGICAL REASONS TO CHOOSE ONE OVER THE OTHERS?

For example:
* v(t) emphasize that the equation will work at various times

* Delta(v) and delta(t) emphasize that changes in v and t are important,
not the actual values.

* "t_f - t_i" emphasizes that you need the beginning and ending time.
(For example, in problems with different acceleration at different parts
of the problem, I find students simply plugging in the final time,
rather than the amount of time elapsed at that particular acceleration).

I find the books are not consistent. For example, they seem to start
with "t_f - t_i" and shift to "t" notation with very little discussion.
Pedagogically, it would be nice to use the same notation as the book,
but not if 1) the book is not consistent itself or 2) the book chose a
very poor option.

(Of course, the same applies to the other equations - e.g. x = x_0 + v_0
t + 1/2 at^2)


Tim F