Re: [Phys-l] Symbols for Kinematics

["R. McDermott" <rmcder@gmail.com>]

In many (most) cases, symbols that represent variables refer to specific 
clock readings : Vi, Vf, etc where initial and final clock readings are 
defined by the problem conditions.  As a result, in many (most) cases, we 
are dealing with an interval of time, delta-T.  As you noted, it has become 
commonplace to drop the delta under the implied assumption that the initial 
clock reading is zero.  Of course, when it is NOT, many students will make 
errors in applying the relevant equations correctly.  From a pedagogical 
point of view, therefore, emphasizing the underlying reality (that this 
refers to a time interval and not a clock reading) is to be preferred even 
though many will not "get" the distinction.  In Modeling, these distinctions 
are dealt with very early on: "position" vs "distance" vs "displacement" and 
"clock reading" vs "time interval".

In any event, I used delta-T and emphasized that we customarily choose two 
positions or two clock readings: start and finish, initial and final, 
original and final, and then used the corresponding symbology.  I can't be 
certain that it helped everyone, but I think it made for improved 
understanding generally.

----- Original Message ----- 
From: "Folkerts, Timothy J" <FolkertsT@bartonccc.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, August 09, 2007 11:18 PM
Subject: [Phys-l] Symbols for Kinematics


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



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