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Re: Derivatives

At 10:08 PM 10/28/97, David Abineri wrote:
I have always pointed out in my Physics classes that a Displacement vs
Time graph must always be differentiable if it is to represent a "real"
situation since one cannot change instantaneously from one velocity to

Today, the question of the differentiability of the Velocity vs Time
graph came into question. It seems to me that this may be non
differentiable, that is to say that acceleration may instantaneously
change from one value to another. HOWEVER, it is difficult for my high
school students to come to grips with this at the intuitive level. I
have shown such graphs to them BUT they seem to be applying their
knowledge of velocity to acceleration incorrectly. I have also said that
an object released from rest suddenly goes from zero acceleration to
9.8m/s/s but I am not sure I have convinced them yet.

Are you sure that the object goes SUDDENLY AND DISCONTINUOUSLY from zero
acceleration to 9.8 m/s/s? Is this a consequence of the Newtonian theory?
Or is it an observation? Or is this an assumption that is derived from the
math representations of the problem?

Richard Grandy
Rice University

Does anyone know of some nice way(s) of getting this point across?

Thanks for any help on this one.

David Abineri

David Abineri

Janice D.Bordeaux, Ph.D.
Center for Technology in Teaching and Learning
230A Mudd Building MS-120
Rice University
6100 Main Street
Houston TX 77005-1892