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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 |
|---|
In fact, the velocity and acceleration are defined as derivatives of the position, a fact acknowledged by the phrase "the calculus of motion". Newton had to invent calculus of one variable to deal with motion\! {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 fact, as you can see, the velocity and acceleration are defined as derivatives of the position, a fact acknowledged by the phrase "the calculus of motion". Newton had to invent calculus of one variable to deal with motion!