To the reader:
The web page found at http://chemweb.richmond.edu/~rubin/pedagogy/131/131notes/131notes_12.html
Was assigned 09/04/02. Students were requested to reduce the
document to its pertinent points and submit them to me. Because
this activity has never come their way, I have provided a sample
summary below.
Rectilinear motion of a particle: position and change of position
Ordinary motion is incredibly complex.
we have focused attention on the most interesting aspect of the
motion and managed to neglect the infinity of complex details
that, at the moment, is irrelevant.
Thus, in some cases, we select an abstraction in which we regard
both clouds and cars as "particles," Successful scientific
inquiry almost invariably starts with an examination of the very
simplest abstractions, building up to more complex situations
as insights are deepened by the initial steps.
To create a numerical description of position of a particle along
a straight line, we set up a series of numerical markers. Denoting
an arbitrarily chosen "origin" point by 0, we mark other
points +1, +2, -1, -2, etc., laying off a coordinate scale of
the kind you should be familiar with from elementary algebra.
The size of the spacing between integer numbers along the line
is arbitrary, and we might adopt any of the standard units of
length available to us through national or international definition.
. For positions in between those marked by integers, we use appropriate
fractional values, for example, at some instant of time a car
on the road may be at position 2.86 on a scale determined by spacing
in miles.
This kind of reference line or coordinate axis is sometimes called
a "reference frame." To describe positions in two- or
three-dimensional space, we erect two or three such axes, usually
perpendicular to each other, to obtain two- or three-dimensional
reference frames.
We choose to use the symbol s to denote any individual position,
and symbols with subscripts (s0, s1, s2, etc.) to denote particular
positions we wish to distinguish from each other. Let's be absolutely
clear about something here: these symbols represent positions
only, not distances traversed by the body. Thus, numbers such
as s1 = +8.63 or s2 = -3.40 indicate locations of a car on the
road, not distances traveled over some period of time.
We are aware of motion of a particle along our reference line
when we find its position changing from instant to instant. Let
us denote a first, or initial, position by s1 and a position at
a later instant by s2. The number s2 - s1 gives us information
about what we might call "change of position." For example,
with the numbers just given, s2 - s1 = -3.40 - 8.63 = -12.03 mi,
assuming the spacing between integer markers is in miles. We will
use the symbol s as a shorthand for the number s2 - s1. That
is,
s s2 - s1,
where s is called "displacement" or "change in
position." The symbol is read as "is defined by"
or "is identical with" or "is equivalent to."
This is not an equation in the sense that y = 3x2 - 2x + 1 is
an equation. Here, it signifies that s is simply a name for s2
- s1.
s, though, has definite algebraic properties: it may be positive,
negative, or zero depending on the numerical values and algebraic
signs of s2 and s1. [