Re: [Phys-l] Symbols for Kinematics

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

John D wrote:

> Here is my attempt to present the basic equations in a way that 
> is self-consistent, reasonably standard, and reasonably tasteful:
>  http://www.av8n.com/physics/intro-acceleration.htm

I like what you wrote on this webpage, but I'm still not convinced that we have reached the best solution.

> Option (a) [delta(v) = v_2 - v_1] is slightly inferior to option 
> (b) [delta(v) = v - v_1], on the grounds that an artist should make 
> the final result look good, even if the intermediate stages don’t look 
> very good.

First of all, what about v_a instead of v_1.  Numerals do a better job emphasizing "initial" and final" but I worry that students might equate v_1 with t=1.  For example, "a car accelerates from t_1 = 0s to t_2 = 1 s" might be confusing.

On the other hand, problems are often broken up into "part a" and "part b".  There is merit in saying "for the interval of time covered in part a, we will define t_1 = 0s and t_2 =10s; for the interval of time covered in part b, t_2 = 10s and t_3 =20s

I had been leaning toward your slightly less favored delta(v) = v_2 - v_1.  I think the symmetry actually is a bigger concern than the slightly simplied final result.  A pretty final result is certainly laudable, but an easier path is also a laudable concern.


But then I thought about graphs.  I think it is MUCH simplier to think of v as "the velocity at any arbitrary time t" and to graph v vs t.  Specific times can then to placed on the graph.  But graphing v_f as a function of time seems somehow perverse.  You would almost need a v_f axis plotted against a t_f axis!


Tim F