h2. Description
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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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{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. 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.
h4. Key to Applicablity
Object moves with *uniform or constant acceleration, v(t) is linear or x(t) is quadratic. * Object has *, constant net force applied,* for instance from gravity.
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
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{latex}\begin{large}$v = v_{\rm i} + a (t - t_{\rm i})$\end{large}{latex}\\
{latex}\begin{large}$x = x_{\rm i}+\frac{1}{2}(v_{\rm f}+v_{\rm i})(t - t_{\rm i})$\end{large}{latex}\\
{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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