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h2. Description
{table:align=right|cellspacing=0|frame="box"|border=1|title=Hierarchy of Models|width=40025%}{tr}h4. Hierarchy of Models{tr}{tr}{pagetree:root=Hierarchy of Models}{tr}{table}
{excerpt}This model applies for a point particle subject to a constant acceleration that is either parallel to or antiparallel to the particle's initial velocity. It is a subclass of the One-Dimensional Motion (General) model defined by the constraint da/dt = 0. {excerpt}
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h2. Assumptions and Limitations

h4. Prior Models
* [One-Dimensional Motion with Constant Velocity]

h4. Vocabulary
* [position (one-dimensional)]
* [velocity (one-dimensional)]
* [acceleration (one-dimensional)]

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h2. Model Specification

h4. System Schema

Internal Constituents:  None.  Object must be treated as a point particle.
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External Agents:  Some constant external influence must be present which produces the acceleration.

h4. Descriptors

Object Variables:  None.
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State Variables:  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.
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Interaction Variables:  Acceleration (_a_).

h4. Laws of Interaction

Acceleration must be a constant.

h4. Laws of Change

{latex}\begin{large}$v_{\rm f} =  v_{\rm i} + a (t_{\rm f} - t_{\rm i})$\end{large}{latex}\\
{latex}\begin{large}$x_{\rm f} = x_{\rm i}+\frac{1}{2}(v_{\rm f}+v_{\rm i})(t_{\rm f} - t_{\rm i})$\end{large}{latex}\\
{latex}\begin{large}$ x_{\rm f} = x_{\rm i}+v_{\rm i}(t_{\rm f}-t_{\rm i})+ \frac{1}{2}a(t_{\rm f}-t_{\rm i})^{2}$\end{large}{latex}\\
{latex}\begin{large}$v_{\rm f}^{2} = v_{\rm i}^{2} + 2 a (x_{\rm f} - x_{\rm i})$\end{large}{latex}

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h2. Relevant Examples

{contentbylabel:1d_motion,constant_acceleration,example_problem|showSpace=false|showLabels=false|maxResults=50}

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