WEBVTT
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Now that we've described the
position vector of the runner,
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let's try to describe
what happens in time
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as a runner moves
along our road.
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Suppose at a later time our
runner has gone down the road
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just a little bit.
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And so the runner has
moved a little bit.
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Remember, at time t, we
described the position vector
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r(t) was equal to the
coordinate function
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x as a function of time i hat.
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And this distance
here was our x(t).
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Now, our position vector
a little bit later.
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So here we are at
time t plus delta t.
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The runner has
moved a little bit.
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And we'll now describe
the position vector--
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because I don't
want to overlap it--
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that center point is up here.
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It's going to point
in this direction.
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And this is what we
call r(t) plus delta t.
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In that vector,
r(t) plus delta t,
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the coordinate function
is no longer at time t
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but t plus delta t i hat.
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And we would now
like to describe
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the displacement vector.
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So our next step is to describe
the displacement vector
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for the interval t
to t plus delta t.
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And that displacement vector
is defined-- we use the symbol
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delta r, and what we
mean is the vector r(t)
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plus delta t minus
the vector r(t).
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Now, what that
vector corresponds to
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is the vector right here.
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This is our delta r.
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And if we now use our
two definitions here,
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then this becomes x(t) plus
delta t minus x(t) i hat.
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And this quantity here we
refer to as the component
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of the displacement vector.
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So delta x is the component
of the displacement vector.
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And as before, the
component can be positive,
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which would correspond
to the person moving
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a positive component,
positive i hat direction,
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in the positive x direction
as shown in this figure.
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If the displacement
of vector is zero,
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the person could
have run forward
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and come back and at
time t plus delta t
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be in exactly the
same spot as time t.
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The displacement vector
is zero in that case.
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The displacement
vector could have
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a component that's negative.
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And what negative means is at
the end of this interval-- t
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plus delta t-- that the person
is to the left of the runner.
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And so this quantity
would be negative.
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And so this is our crucial
displacement vector that
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describes only the difference
in positions between the person,
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between time t plus
delta t, and time t.