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

{excerpt:hidden=true}System: [Point particle|point particle]        Interactions: Any{excerpt}

{excerpt}This model is technically applicable to any [point particle].  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.{excerpt}


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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System: One point particle. — Interactions: Any.
Description and Assumptions
This model is technically applicable to any point particle moving in three dimensions, and involves vector calculus. Except for circular and rotational motion, however, one generally treats the vectors in Cartesian coordinates, so they split into three one-dimensional equations, allowing a solution with three applications of the One-Dimensional Motion (General) model.
Problem Cues
This model is needed only for problems that clearly involve motion in three dimensions, and is not often used in introductory mechanics.
Model
Compatible Systems
A single point particle (or a system treated as a point particle with position specified by the center of mass).
Relevant Interactions 
Only knowledge of the net external force is required to determine the acceleration of the system. 
Laws of Change
The laws of change are simply the laws of calculus for vectors. 
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Differential Forms
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\begin{large}\[ \frac{d\vec{v}}{dt} = \vec{a}\]\end{large}
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\begin{large}\[ \frac{d\vec{x}}{dt} = \vec{v}\]\end{large}
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Integral Forms:
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Integral Forms
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\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}
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{latex}\
\begin{large}\[ \vec{x}(t) = \vec{x}(t_{0})+\int_{t_{0}}^{t} \vec{v}\;dt\]\end{large}
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h2. Relevant Examples

None.
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Relevant Examples
None yet. 


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