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

{excerpt}Technically, 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, 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 situation where the net [force] on the system is constant (a point particle subject only to near-earth [gravity] is a common example).  It is a subclass of the [One-Dimensional Motion (General)] model defined by the constraint da/dt = 0. {excerpt}

h2. Problem Cues

For pure kinematics problems, the problem will often explicitly state that the acceleration is constant, or else some quantitative information will be given (e.g. a linear velocity versus time plot) that implies the acceleration is constant.  This model is always applicable to the vertical direction in a problem that specified gravitational [freefall].  The model is also sometimes useful (in conjunction with [Point Particle Dynamics]) in dynamics problems when it is clear that the net force is constant.

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h2. Prerequisite Knowledge

h4. Prior Models

* [1-D Motion (Constant Velocity)]

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

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. Interaction Variables

Acceleration (_a_).

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h2. Model

h4. Laws of Change

This model has several mathematical realizations that involve different combinations of the 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. Diagrammatical Representations

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

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h2. Relevant Examples

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