Re: kinematics, traditional or not

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

> -----Original Message-----
> From: Tim Folkerts [mailto:tfolkert@FHSU.EDU]
> Sent: Monday, August 26, 2002 2:17 PM
> [snip]
>
> The kinematic equations are merely mathematical definitions.  After
> DEFINING
> v==dr/dt and a==dv/dt , you can use calculus to DERIVE  x = 1/2at^2 +
> v(0)t+ x(0), etc for constant acceleration, or DERIVE a = v^2/r for
> circular motion.  This has nothing to do with forces.

You are right.  However, the question (at least as I see it) is about
motivation.  Why would one want to define v and a?  Why would one want to
derive expressions that assume a constant acceleration?  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.

I think one can do it either way.  In my case, my plans (for the fall) are
to first lead the students through the empirical exercise of defining speed
in order to describe motion.  Rather than repeat the exercise with the more
complicated motion associated with free-fall, I've decided to use Newton's
laws to illustrate the power of developing a generalized model (by applying
them to free-fall).  This is why I have chosen to do option (2).

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