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Re: [Phys-l] Symbols for Kinematics



First let me comment about consistency in symbols. If you are going to use V0 as the initial velocity, then it seems to me you should be using t0 as the initial time and in your first equation you should be using t-t0 instead of just t. Similarly since you don't used vf for v final, why would you tf for t final. I think there is something to be said for consistency especially when you are working to make the connection between concrete events and conceptual entities via the use of symbols.

Regarding the pedagogy...a very important issue...I don't know of any research that would point to one formalism over another...perhaps others do. Having none, I would focus on what you want the students to understand and use that as a guide.

So if you want to make the point that velocity values are dependent on the frame of reference, you might want to emphasize changes in velocity and write the equation as
v - v0 + a(t-t0). Or you might want to start with a simpler form and evolve into a more complete form as the richer physical context might demand.

There is always a problem with differing from the text, while the students might not read it in depth unless you force them in some way, they will of course take the equations as bible and simply as the only way to calculate a number. In my experience they don't see equations as sentences that relate concepts.

So here is an idea to get students to think about equations as more than tools to calculate a number. Ask them the same question you asked the list, early on, when you hit the first kinematic equation. Perhaps the discussion will begin to change their perspective on what an equation is. Just an idea that your note suggested.

joe

Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Aug 9, 2007, at 11:18 PM, Folkerts, Timothy J wrote:

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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