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Serway faces the same problem that all textbook authors must at some point: Is it better to cover motion first or vectors first? Motion engages the students quickly and easily. One can do lots of simple experiments and demonstrations that can make the concepts of motion more concrete. However, the transition from 1D to 3D becomes awkward because components have signs but vectors do not. Starting with vectors turns the students off almost immediately - once they are turned off it's almost impossible to get them back. Serway take a middle ground of 1D, vectors, then 3D - but does it very clumsily. When students find that vectors don't have signs but components do, they have to unlearn terminology used for 1D motion.
I basically take the approach Tim has taken - warn the students that what is called a vector in the 1D chapter will be viewed as a component of a vector later on. It would have been better if the word vector simply wasn't mentioned - one can still differentiate between velocity and speed without it in 1D.
Our department has used Serway for many years. I have become a little lazy about reviewing other texts that might have a better approach.
Bob at PC
________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Folkerts, Timothy J
Sent: Sat 8/11/2007 5:00 PM
To: Forum for Physics Educators
Subject: [Phys-l] Motion in 1D, vectors and vector components
Along with my previous efforts to decide how to write symbols for kinematic parameters, I have also been struggling with how to deal with 1D motion. The book I am using (Serway) seems to really botch things up. Basically, the whole chapter about 1D motion uses the word "vector" when they usually actually mean "x-component of the vector".
For example:
" Average velocity can be either positive or negative."
" The average velocity is equal to the slope of the graph of position vs time."
" The graph of velocity vs time..."
The X-COMPONENT OF VELOCITY can be positive or negative.
The X-COMPONENT OF VELOCITY is the slope of x vs t.
The X-COMPONENT OF VELOCITY can be plotted on a graph.
Serway even admits that he botched the treatment of vectors in 1D when he gets to the chapter on 2D: "This simple solution (using signs to indicate direction) is no longer available in 2 or 3 dimensions. Instead, we must make full use of the vector concept." In other words, he didn't do things right the first time!
I expect that other books are similar.
How picky should we be? Is it so incorrect to say "plot v vs t" or "velocity vs time" that it should be avoided? Even assuming that "v" is the magnitude of velocity - rather than the true vector velocity - is not right, because | v_vector | is always positive, but we are perfectly comfortable plotting negative values on the graph.
Sticking to "v_x" or "x-component of velocity" the whole time would seem to solve the problem without being too burdensome to either the instructor or the students
I am currently planning:
1) to do vectors first from Ch 3 and discuss components of vectors
2) to cover 1D motion from Ch 2, but be more careful about the terminology
3) to finish Ch 3 and 2D motion.
Tim F