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h2. Keys to Applicabilty

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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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{table}{excerpt}ThisTechnically, this model is applicable to a single [point particle] subject to a constant acceleration that is either parallel to or anti-parallel to the particle's initial velocity.  It will, but its real usefulness lies in the fact that it can describe mutli-dimensional motion with constant acceleration by separate application to orthogonal directions.  Thus, it can be used describe the system's motion in any situationssituation where the net [force] on the system is constant (a point particle subject only to near-earth [gravity] is a common example).  The model can be used to describe mutli-dimensional motion by separate application to orthogonal directions.  It is a subclass of the [One-Dimensional Motion (General)] model defined by the constraint da/dt = 0. {excerpt}

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h2. Assumed Knowledge

h4. Prior Models

* [1-D Motion (Constant Velocity)]

h4. Vocabulary

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

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h2. Model Specification

h4. System Structure

*[Constituents|system constitutent]:*  [Point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).

*[Interactions|interaction]:*  Some constant external influence must be present which produces a constant acceleration that is directed parallel or anti-parallel to the particle's initial velocity.

h4. Descriptors

*[State Variables|state variable]:*  Time (_t_), position (_x_) , and velocity (_v_) are possible state variables.  Note that in some cases only two of the three possible state variables will be needed.

*[Interaction Variables|interaction variable]:*  Acceleration (_a_).


h2. Model Equations

h4. Mathematical Statement of the Model

This model has several mathematical realizations that involve different combinations of state variables.
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{latex}\begin{large}$v =  v_{\rm i} + a (t - t_{\rm i})$\end{large}{latex}\\
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{latex}\begin{large}$x = x_{\rm i}+\frac{1}{2}(v_{\rm f}+v_{\rm i})(t - t_{\rm i})$\end{large}{latex}\\
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{latex}\begin{large}$ x = x_{\rm i}+v_{\rm i}(t-t_{\rm i})+ \frac{1}{2}a(t-t_{\rm i})^{2}$\end{large}{latex}\\
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{latex}\begin{large}$v^{2} = v_{\rm i}^{2} + 2 a (x - x_{\rm i})$\end{large}{latex}

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h2. Relevant Examples

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