Re: Magnitude of average velocity

[Bob Sciamanda <trebor@VELOCITY.NET>]

> When I ask students to calculate the magnitude of the average velocity
for a
> simple projectile problem (e.g., ball thrown horizontally from a roof),
they
> often simply add the initial and final speeds and divide by 2. . .
> . . . 2) Why
> is the quantity they are calculating not even the correct average speed?

Use examples:
The average value of the integers 1,2,3,4,5,6,7,8,9,10  is indeed half the
sum of the first and the last.
The average of the integers 1,5,7,8,9 is 6 , but half the sum of the end
values is only 5.

Now have the students add their own examples. Then let them then struggle
toward the reason for the different behavior. (the uniform rate of change
in the first example).

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Lemmerhirt, Fred" <FLemmerhirt@MAIL.WCC.CC.IL.US>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, September 19, 2001 1:12 PM
Subject: Magnitude of average velocity


.  They no
> doubt think, "when acceleration is constant (as it is in projectile
motion),
> this is how you can calculate average velocity (in one dimension); and
speed
> is the magnitude of velocity, right?"
>
> Does anyone have a good brief intuitive explanation (for beginning
> calculus-based-physics students) of the reason(s) that this doesn't
work?
> (or maybe a  reference to a particularly good textbook explanation)
>
> I suppose this is a two-part problem:  1) Why is the average of the
> magnitude of a vector not the same as the magnitude of the average?  >
[Since this is somewhat related to the current discussion entitled
> "Problem", which I haven't been following in complete detail, I hope
this
> request doesn't duplicate something that was just covered there.]
>
> _____________________________
> Fred Lemmerhirt
> Waubonsee Community College
> Sugar Grove, Illinois
> flemmerhirt@mail.wcc.cc.il.us
> http://chat.wcc.cc.il.us/~flemmerh/physics.html