Re: (d/dt)ACCELERATION

[John Denker <jsd@MONMOUTH.COM>]

David Abineri wrote:

> >  It seems that it
> > is possible for an object to go from one acceleration (slope) to another
> > instantaneously.  When releasing an object to free fall the acceleration
> > goes from 0 to 9.8 at the instant it is released does it not?

There are very few things in physics that are truly discontinuous.  (There
are various discontinuities that arise in the theory of phase transitions
-- but only in the thermodynamic limit (infinitely large systems) and
subject to various other provisos.)

Sometimes we talk about collisions in a "hard-sphere" gas, but real gasses
are not hard spheres.  The Lennard-Jones potential is continuously
differentiable at the points of interest.

At 07:58 AM 9/14/00 -0400, Ludwik Kowalski wrote:
> It takes time to "release" something; perhaps as little as one ms, or so.
> During that time the net force is increasing gradually.

Consider a steel ball colliding with a steel plate.

An important timescale here is set by the speed of sound and the size of
the object.  For steel, c is about 5000 m/s, so for a half-cm steel ball
the timescale is a microsecond.

For times short compared with this timescale, we cannot even speak of "the"
velocity of the object.  If the front of the ball has started to collide,
the back doesn't even find out about it until a microsecond later.

OTOH if you want to talk about the force on the front layers of the ball,
that changes over a very short timescale -- nanoseconds or less.  That's
still not quite instantaneous, but it's pretty fast.

============

BTW there is a colorful name for the derivative of acceleration.  We have
  0) position
  1) velocity
  2) acceleration
  3) jerk