Re: Spring potential energy without Work (sort of)

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

Robert C. wrote in part (quoting Joel R)
> > I readily admit that formally the arguments are identical.
>
> I know you feel it is a matter of taste but I'm curious as to why
> you think the result is less natural for Delta x^2?

It is not a strongly held belief, and I may likely change my mind as your
post got me thinking along these lines; and I do think this opinion is a
matter of taste.

Often derivations in physics are motivated from knowing the result, a kind
of a posteriori motivation rather than an a priori motivation.  I am
thinking that the Delta X^2 derivation is of this type.

OTOH I think the Delta V^2 derivation can be a priori motivated.  (at least
this is what I was thinking on Monday)

As follows:

1) consider constant acceleration situations

2) its easy to show v vs. t, it a straight line after all so we establish v
as a function of t.

3) Kinematics, among other things, is about where a particle is located; so
it is natural to inquire as to what x(t) is.  That results in the use of the
averaging operation you described.

4) I now have two equations relating three quantities x,v,t through the
parameter a.  I think it is  natural to use those two equations to eliminate
one of the quantities. Thus arriving at the Delta V^2 relation.

That's all, nothing profound.