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{td:alignwidth=center350px|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Description and Assumptions

{excerpt:hidden=true}*System:* One [point particle] constrained to move in one dimension. --- *Interactions:* Any that respect the one-dimensional motion.{excerpt}

This model is applicable to a single [point particle] subject to an acceleration that is constrained to one dimension and which is either parallel to or anti-parallel to the particle's initial velocity.


h2. Problem Cues

In practice, this model is only useful when a one-dimensional acceleration is given that has a _known_ time dependence that is _not_ sinusoidal.  If the acceleration is constant, the sub-model [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)] should be used.  If the acceleration is sinusoidal (described by a sine, cosine, or sum of the two), the sub-model [Simple Harmonic Motion] should be used.  Thus, in practice, the problem cue for this model is that the acceleration will be given as an explicit and integrable function of time, most often a polynomial (the acceleration might also be plotted as a linear function of time).  

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h2. Prerequisite Knowledge

h4. Prior Models

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

h4. Vocabulary

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

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h2. System

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

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h2. Interactions

Some time-varying external influence that is confined to one dimension.

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h2. Model

h4. Laws of Change

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h5. Differential Forms
{latex}\begin{large}\[ \frac{dv}{dt} = a\]\end{large}{latex}\\
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{latex}\begin{large}\[ \frac{dx}{dt} = v\]\end{large}{latex}\\
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h5. Integral Forms
{latex}\begin{large}\[ v(t) = v(t_{0})+\int_{t_{0}}^{t} a\;dt\]\end{large}{latex}\\
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{latex}\begin{large}\[ x(t) = x(t_{0})+\int_{t_{0}}^{t} v\;dt\]\end{large}{latex}\\
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h2. Diagrammatic Representations

* Acceleration versus time graph.
* Velocity versus time graph.
* Position versus time graph.

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h2. Relevant Examples

None yet.
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