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Re: kinematics, traditional or not



I'm sorry I wasn't clear in my previous note.

However, the question (at least as I see it) is about
motivation. Why would one want to define v and a?

How can you avoid defining v & a??? To use something you
need to have a
common understanding. You can't even know if F = ma unless
you know what
the terms are.

*You* know why defining v and a are useful. *I* know why defining them is
useful. Everyone on this list knows why defining them is useful.

My point is that the *students* don't.

Yes, defining v and a is needed to derive the kinematic equations. Yes, you
can't know F=ma unless you know what the terms are. However, my point is
that it must be clear to the students *why* and just stating that "you will
need to use them later for things like F=ma (which you don't understand
right now) or x=vt+.5at^2 (which you also don't see a need for right now)"
just doesn't work.

Why would one want to derive expressions that assume a constant
acceleration?

You don't need to derive the constant acceleration equations. They
certainly aren't somehow fundamental. v == dx/dt and a ==
dv/dt. That's
it. That IS kinematics. You can _describe_ any motion in
terms of those
equations.

Why not define da/dt? Is it clear to your students why you stopped at
dv/dt?

That said, with these definition you can then explore their
ramifications.
WHAT IF the acceleration is constant... WHAT IF the motion
is circular...
WHAT IF acceleration is proportional to distance... These
are just a few
interesting examples of the what the definitions predict.

Yes, if one knows the acceleration, one can use the definitions of v and a
to get x and v. But, again, is it clear to your students why one would more
likely know the acceleration than anything else?

It seems to me that one can either:
(1) examine a case of free-fall empirically, which leads you
to define
acceleration in order to describe the motion, and then use
the finding
that
free-fall is characterized by constant acceleration to derive an
expression
for x; or
(2) examine what happens when a force is applied, which leads you to
Newton's 2nd law, and then use the assumption that gravity
is the only
force
acting during free-fall to predict a constant acceleration
and derive an
expression for x in order to test that prediction.

But how do you "derive an expression for x"? You define a ==
dv/dt and v
== dx/dt and integrate. You still need to derive the exact
same equations
for constant x that you thought weren't worth deriving.

Again, *I*, like *you*, think they are worth deriving. But do the students?
How do you structure your course so that the students see their value
(without resorting to "you will see the need later")?

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301