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Definitions of Position and Velocity 
If
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we
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start
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knowing
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the
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position
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vs.
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time
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x ( t ),
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then the
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velocity,
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v ( t )
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, is
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the
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derivative
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of
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its
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position,
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and
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the
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derivative
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in turn of
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this
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velocity
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is
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the
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particle's
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acceleration,
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a ( t ).
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The
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force
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is
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the
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particle's
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mass
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times
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a ( t ).
| Latex |
|---|
}\begin{large}\[ v = \frac{dx}{dt} \]\end{large} |
| Latex |
|---|
\begin{large}\[ a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}\]\end{large}{latex} |
In
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fact,
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as
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you
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can
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see,
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the
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velocity
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and
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acceleration
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are
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defined
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as
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derivatives
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of
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the
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position,
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a
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fact
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acknowledged
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by
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the
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phrase
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"the
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calculus
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of
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motion".
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Newton
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had
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to
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invent
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calculus
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of
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one
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variable
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to
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deal
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with
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motion
...
!
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