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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Description and Assumptions

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

This model is technically applicable to any [point particle] system.  In practice, however, the vector equations in this model are usually split into three one-dimensional equations, so that the [One-Dimensional Motion (General)] model is nearly as general, and more easily used.


h2. Problem Cues

This model is rarely needed in introductory mechanics, and is presented principally for intellectual completeness of the hierarchy.

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h2. Prerequisite Knowledge

h4. Prior Models

* [1-D Motion (Constant Velocity)]
* [1-D Motion (Constant Acceleration)]
* [One-Dimensional Motion (General)]

h4. Vocabulary

* [position (one-dimensional)]
* [velocity]
* [acceleration]

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h2. System

h4. Constituents

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

h4. State Variables

Time (_t_), position (_x_) , and velocity (_v_).

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h2. Interactions

h4. Relevant Types

Any.

h4. Interaction Variables

Acceleration (_a_(_t_)).

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h2. Model

h4. Laws of Change

Differential Forms:
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{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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Integral Forms:
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{latex}\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}{latex}\\
\\
{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.
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