h2. Description
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=40%}{tr}{td:align=center|bgcolor=#F2F2F2}*Hierarchy of Models*{td}{tr}{tr}{td}{pagetree:root=Hierarchy of Models}{td}{tr}{table}
{excerpt}This model is applicable to a point particle subject to a constant acceleration that is either parallel to or anti-parallel 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 Structure
Internal Constituents: Point particle.
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Environment: 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
Object Variables: None.
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.
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
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