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I guess I would argue that while Bob is correct mathematically, physically
you still can't have a changing velocity and a zero acceleration. That is,
the instantaneous quantities (the derivatives) are abstract and (at least)
operationally are not 'real'. A CHANGE requires a non-zero time interval.
That interval can be small, it can approach zero, but the derivatives just
tell us the LIMIT as the delta-t goes towards zero. In the physical world,
we really can't perceive or measure a zero time interval. Since the
definition of acceleration is delta-v/delta-t, if delta-v is non-zero, then
the acceleration can't be zero. The _limit_ as delta-t goes towards zero
can be.
So, I would say that in an abstract, mathematical sense, Bob's examples are
OK, but in any practical, physical sense, Seth's statement still holds. I'm
willing though to consider a 'real world' example that would support Bob's
mathematical argument--one that has physical significance for a = 0, delta-v
not = 0.
Rick
*********************************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
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********************************************************
----- Original Message -----
From: "Bob Sciamanda" <trebor@WINBEAM.COM>
Seth wrote:
| If the object is to change its velocity it must have a non-zero value
for
| acceleration; i.e. to change one's velocity requires an acceleration
(either
| by changing one's speed or direction).
Consider the displacement y(t):
(Think of it as a vertically tossed ball on a very strange planet!)
y(t) =200t/3 - 5t^2 + (t^3)/6 - (t^4)/480
Take three derivatives and plot y(t) , v(t) , a(t) and j(t) from t=0 to
40.
Observe that the thing seems to "hang" momentarily at y=333.33:
At t=20 the object has reached the top of its path. It then turns around
and
falls.
But at t=20, the velocity, the acceleration and the jerk are ALL zero!
It only keeps going (turns around) because the derivative of its jerk is
non-zero (-1/20). ALL other derivatives of y(t) are zero at t = 20.
This should disabuse one of (sometimes spoken, sometimes implied)
arguments
that the acceleration (and/or jerk) cannot be zero at a turnaround point
simply because the velocity is obviously changing.
You can concoct for yourself more bizarre (but possible) motions in which
the velocity keeps changing even though (at some time) it and all of its
derivatives but the Nth one are zero, N being as large as you please.