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Definitions
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of
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Position and Velocity 
If we start knowing the position vs. time x ( t ), then the velocity, v ( t ), is the derivative of its position, and the derivative in turn of this velocity is the particle's acceleration, a ( t ). The force is the particle's mass times a ( t ).
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and Velocity [!copyright and waiver^SectionEdit.png!|Motion -- 1-D General (Definitions)] If we start knowing the position vs. time {*}x ( t ){*}, then the velocity, {*}v ( t ){*}, is the derivative of its position, and the derivative in turn of this velocity is the particle's acceleration, {*}a ( t ){*}. The force is the particle's mass times {*}a ( t ){*}. {latex}\begin{large}\[ v = \frac{dx}{dt} \]\end{large}{latex} \\ {latex} |
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\begin{large}\[ a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}\]\end{large}{latex}
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In
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fact,
...
as
...
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
...
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
...
with
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motion
...
!
...