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We will now like to begin
our analysis of motion.
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And we'll start with
one dimensional motion.
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Let's just consider a
person running along a road.
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And so here's our runner,
and here's our road.
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And what we want to do
is be able to describe
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the position, the velocity, the
acceleration of this runner.
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In order to do that, we need
our first mathematical tool,
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which is a coordinate system.
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What is a coordinate system?
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Well, the first thing that we
want to choose is an origin.
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We can pick the origin
anywhere we want.
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That's a degree of freedom.
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So let's choose a point
along our road as our origin.
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The next thing to do
is to choose an axis.
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Well, the road is
naturally defining
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an axis for our problem.
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And so we'll call
this the x-axis.
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Now, along with
that axis, we want
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to divide that up into
some type of units
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so we might divide
our axis like this.
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And what's important
here is to introduce
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a positive coordinate direction.
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And so the way I'll do that,
is I'll call this the plus x,
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and on this side of the
origin x is negative.
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Now, the third most
important thing
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is that we're going to talk
about vectors and physics.
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So we want a choice
of unit vector.
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Now, because it's only
one dimensional motion,
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we only need one unit vector.
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So what that means is a choice
of unit vector at every point.
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Let's just consider
a point here, P1.
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So our unit vector
I'll call it i hat 1.
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Now, let's pick
another point here.
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We'll call this the point P2.
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And over here we'll choose
a unit vector, i hat 2.
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So every single point in
space has a unit vector.
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Now, what's unique
about this one
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dimensional linear
Cartesian coordinate
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system is the following,
these unit vectors
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have the same magnitude--
a unit vector by definition
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has magnitude 1-- and they're
pointing in the same direction.
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So if two vectors have
the same magnitude
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and point in the same
direction, they are equal.
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So what makes this
coordinate system unique,
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this Cartesian
coordinate system,
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that every single point,
no matter where we are,
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the unit vectors point
in the positive direction
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because they have the same
magnitude and direction.
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All of these unit
vectors are equal.
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And we call that i hat.
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So symbolically, we
may draw a picture
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and indicate our unit vector
in the positive x direction.
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And this is our
coordinate system.
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And we can next
begin to describe
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the position and the
velocity of our object
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as it's moving along
this x direction.