Re: The "basic three" (was: Re: Scientific method was physical pendulums/ an opportunity)

[Doug Craigen <dcc@ESCAPE.CA>]

John Mallinckrodt wrote:
> On Thu, 30 Sep 1999, Doug Craigen wrote:
>
> > ... the thing I [emphasize] is that the basic three allow them to solve
> > anything (and d=vo*t + 1/2 a*t^2 is not on the list)
>
> Hmm; a provocative comment.  Am I wrong in assuming that your
> "basic three" are
>
> delta x = v_ave * delta t
> v_ave = (v_i + v_f)/2
> a = delta v/delta t

Very good, though the way I present it would be more like:

we have two basic physical quantities in kinematics - time intervals and
displacement.  We *define* velocity by v_ave = displacement/time
interval and we *define* acceleration by a_ave = change in velocity/time
interval (I also mention jerk, snap, crackle and pop as a side-note for
a good laugh from the class).  So many students take physics and miss
the fact that this is all there is to kinematics and everything else
follows from there by mathematical details (vector components, the
meaning of "instaneous" etc).  For example, the third "fundamental"
equation comes from looking at a graph of velocity versus time under
constant acceleration to see that in that case
v_ave = (v_i + v_f)/2

For me it is satisfying to see students solve problems from nothing but
the simple equations above when (as is often the case) it is more
convenient than  d = vo*t + 1/2 a*t^2 etc.  Admittedly though, in a
calculus based class one might prefer to present this as a fundament
equation (ie. velocity, acceleration, jerk etc are the names of the
derivatives in the Taylor coefficients of the equation for displacement
as a function of time) but I've usually taught non-calc so I've not
thought through my preferences for that case.

()-()-()-()-()-()-()-()-()-()-()-()-()-()-()-()

Doug Craigen
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