Re: That jerk again!

[John Gastineau <gastineau@mindspring.com>]

Sorry, somehow a message got sent before I finished. See below for the full
message.

At 06:43 PM 11/19/97 -0600, Brian Whatcott wrote:
> At 11:54 11/19/97 -0500, John Gastineau wrote:
>
> > In rolling the car up a hill, it matters not when you jam on the brakes
(at
> > the top or before); you are introducing a sudden change in acceleration, a
> > jerk, and we feel that pressure change. It is simply surprising to have it
> > happen at zero velocity. The value of the velocity at a given instant has
> > nothing to do with its first or second derivative.  
>
> A person who bases his conclusions on experimental tests is not to
> be trifled with; but I fancy he overreached his data - or wrote a little
> hastily when he claims that the value of the velocity [ when the brakes are
> applied] has nothing to do with the consequential acceleration, or ITS
rate...
> John will easily agree that he could reverse the sign of the acceleration
> caused by braking by choosing his moment on the velocity slope of constant
> deceleration...

Ok, Ok, I was sloppy. What I was trying to say was that the value of a
parameter, say, velocity, at one moment in time, is independent of the value
of its rate of change. This is true in general, and can be seen in the
necessity of specifying both an object's location and velocity to completely
specify its condition. I emphasize that this is at just a moment in time. 

It is true, as Brian points out, that one can determine the sign of
acceleration by varying when we apply the braking force. That's a
characteristic of the friction force, which switches direction when the
velocity changes sign. 

But knowing the velocity does not allow us to infer the acceleration, nor
does knowing the acceleration allow us to infer the jerk. The latter is what
some are trying to do here, and the error is the same as the one of
beginning students who insist that since the velocity is zero at the top of
the coin toss, the acceleration must be zero as well. 

(Aside: I consult for several multimedia production companies. A programmer
really really wanted to change a graph so that the acceleration at the top
of a coin toss animation was zero. He was so sure...)

JEG



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John E. Gastineau      gastineau@mindspring.com               KC8IEW
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