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Re: da/dt = jerk?



As you report it, it seems Arons is defining jerk differently from
how I have usually heard it defined. The usual definition is that
jerk is the rate of change of acceleration, not just the change in
acceleration.

Oddly enough I asked exactly the question Arons treats a couple of
years ago in this group, and it was answered quite satisfactorily
at that time. In the driver's frame of reference we need only
consider the vertical component of the acceleration. While rolling
freely uphill the acceleration of gravity perceived by the driver
is less than it is in the car at rest. The chassis rides higher on
its suspension than it would at rest, and the driver does not
compress his seat as much as he would at rest (John Denker and
Roger Freedman will know this well from the more extreme versions
they encounter flying airplanes). As a result, when the car comes
to a stop and the tires are suddenly clamped to the pavement, the
car settles on its suspension and the driver settles even further
into his seat cushions.

Now it is true that there is a jerk involved here, but it has
(ideally)infinite magnitude. The magnitude of the jolt felt is not
related directly to to the magnitude of the jerk; "jolt", if I may
coin a physical quantity, is the change in acceleration, delta a,
and is unrelated to the rate of change so long as the time interval
involved is sufficiently short.

Arons's comment about the same effect on a horizontal road is a
little more difficult to understand. If one coasts to a stop on a
horizontal road the same effect will be felt. The reason, of
course, is that there is still an abrupt change of acceleration
involved. The effect is smaller, of course, but it is quite
perceptible. Arons (who has been a guest in our home) has a nice
place in the mountains, by a river in neighboring Washington. He
may be used to rough roads like the one that leads to his place,
and the jolt associated with the gentler horizontal example may
have escaped his notice.

I hope this helps.

Leigh