Re: Kinematics

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding John Denker's comment:

> The intermediate-value theorem says that there must
> be *some* t in the interval [t1,t2] where the velocity
> equals Vav.  Similarly there must be *some* x in the
> interval [x1,x2] where the velocity equals Vav.  But
> there is !!not!! any good reason to assume that the
> special point is the middle of the t-interval or the
> middle of the x-interval.

How about this reason?  The choice of the midpoint of the (t- or x-)
interval minimizes the maximum error in the estimate of the location
of this intermediate value where the Vav value is locally correct,
and bounds it to be no more than 1/2 of the interval's width.

Maybe it is not a "good" reason in John's judgment, but it seems to
be a reason of some sort, nonetheless.

David Bowman