Re: Derivatives

[Bob Sciamanda <sciamanda@worldnet.att.net>]

Dave,
     This has bothered me for some time.  Can a real force be applied 
discontinuosly, so that the "jerk" is infinite?  I think this can only 
be answered by careful experiment for each proposed case. 
But, gedanken-wize, I tend to agree with the students.  
It would seem that if you examine the process 
sub-microscopically (in time and space) you would see a "gradual" 
diminution of your supporting force as you release an object into free
fall.
A fertile field for experimentation!

David Abineri wrote:
> I have always pointed out in my Physics classes that a Displacement vs
> Time graph must always be differentiable if it is to represent a "real"
> situation since one cannot change instantaneously from one velocity to
> another.
>
> Today, the question of the differentiability of the Velocity vs Time
> graph came into question. It seems to me that this may be non
> differentiable, that is to say that acceleration may instantaneously
> change from one value to another. HOWEVER, it is difficult for my high
> school students to come to grips with this at the intuitive level. I
> have shown such graphs to them BUT they seem to be applying their
> knowledge of velocity to acceleration incorrectly. I have also said that
> an object released from rest suddenly goes from zero acceleration to
> 9.8m/s/s but I am not sure I have convinced them yet.
>
> Does anyone know of some nice way(s) of getting this point across?
>
> Thanks for any help on this one.
>
> David Abineri
>
> --
> David Abineri     dabineri@dot-net.net

-- 
Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
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