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Re: [Phys-L] Sequence



I used to think that graphs helped students understand the relationship between position, velocity and acceleration I've since learned that students have just as much trouble with graphs as with equations, so introducing graphs at the same time as the relationships does not help them.

It is for this reason that we start with motion. Students can tell when objects are moving. They can't tell if a falling object is speeding up, though. So, we start with objects at rest and discuss how the net force on the object is zero in that case. We then examine what happens to the object, starting at rest, if the net force is not zero. We use a motion sensor to plot the velocity. They see that the velocity increases at a constant rate as long as the net force remains the same.

We do not introduce the word acceleration at this point, as we know they confuse that word with velocity. Besides, it is unnecessary.

We then examine what happens to the object if it is NOT starting at rest. Again, there is no need to introduce acceleration or displacement.

Only after thoroughly examining the relationship between the net force and the CHANGE in velocity (in one dimension, using positive and negative), do we explore how to predict the displacement. We don't derive the kinematic equations. Instead, we have students predict the displacement by first identifying the forces, then identifying the change in velocity (using N2L), then identifying the average velocity (assuming constant forces), then using the definition of average velocity to get the displacement.

After that, we explore 2-D motion.

After that, we introduce momentum, acceleration and work, as three alternate ways of describing what is going and making predictions, comparing the three in terms of their advantages and disadvantages relative to each other.

------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University
East Stroudsburg, PA 18301
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of Philip Keller [pkeller@holmdelschools.org]
Sent: Wednesday, March 19, 2014 9:17 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Sequence

I spend weeks on this all as well! It may be the thing that Hewitt said
that I most agree with: kinematics can be a black hole right at the
beginning of the course.

But what if the ONLY things you wanted to get across were:

PART I -- here is one kind of motion we care about.
1. When an object moves at a constant speed in a straight line, its
position graph is a line.
2. In that case, the slope of that line stays constant. That slope is
the speed.
3. Since the speed is not changing, the "velocity" graph is a
horizontal line.

PART II--here is another motion we care about.
1. Sometimes, velocity graphs increase or decrease in a linear manner.
2. In that case, speed is changing. The position graphs curve up
(showing increasing speed) or down (showing decreasing speed).
3. The slope of that linear speed graph is called "acceleration".

Suppose we stop right there (for now). No equations. No word
problems. Nothing about area under v vs t. No discussions of positive
vs negative velocity and acceleration. No debates about the
acceleration of an object at its peak. No debates about "deceleration"
vs negative acceleration. No discussion of vectors. All of that can
wait. For now, velocity is just our fancy-pants word for speed.

That's what I think can be done in just a few periods. But again, I was
thinking out loud. I have not tried this approach.



On 3/19/2014 8:22 PM, Marty Weiss wrote:
3 class periods? really? usually takes weeks to get those points across.
all those other concepts in a short period of time? months here!

On Mar 19, 2014, at 7:53 PM, Philip Keller wrote:

Just thinking at loud here...

What if you start by defining constant velocity and showing what its
position and velocity graphs look like. Then define constant, non-zero,
positive acceleration and show what its position and velocity graphs look
like. At this point, you have invested maybe 3 class periods if you go
slow.

Then move on to forces, momentum, energy, circular motion, gravitation,
whatever you like, returning to kinematics as later, say before you teach
projectile motion but after you teach vectors.

This way, you would have the vocabulary of kinematics in place but not the
equations. You would get to say things like: when no unbalanced forces act
on an object, its velocity graph looks like this,or like this but never
like that.

It feels to me that you could teach a lot of physics before you needed any
further kinematics treatment.


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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l