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{excerpt:hidden=true}*System:* One [point particle|point particle]. --- *Interactions:* Any.{excerpt}

h4. Description and Assumptions

This model is technically applicable to any [point particle] system.  In practicemoving in three dimensions, and involves vector calculus.  Except for circular and rotational motion, however, one generally treats the vectorvectors equations in thisCartesian modelcoordinates, areso usuallythey split into three one-dimensional equations, so that allowing a solution with three applications of the [One-Dimensional Motion (General)] model is nearly as general, and more easily used.

h4. Problem Cues

This model is rarely needed needed only for problems that clearly involve motion in introductorythree mechanicsdimensions, and is presentednot principallyoften forused intellectualin completeness of the hierarchyintroductory mechanics.


h2. Model

h4. Compatible Systems

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).


h4. Relevant Interactions 

Only knowledge of the [net|net force] [external force|external force] is required to determine the motionacceleration of the system.  


h4. Laws of Change

The laws of change are simply the laws of calculus for vectors. 

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h5. Differential Forms
{latex}\begin{large}\[ \frac{d\vec{v}}{dt} = \vec{a}\]\end{large}{latex}\\
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{latex}\begin{large}\[ \frac{d\vec{x}}{dt} = \vec{v}\]\end{large}{latex}\\
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h5. Integral Forms
{latex}\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}{latex}\\
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{latex}\begin{large}\[ \vec{x}(t) = \vec{x}(t_{0})+\int_{t_{0}}^{t} \vec{v}\;dt\]\end{large}{latex}\\
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h2. Relevant Examples

None yet.
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