Page History

h2. Keys to Applicabilty

{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=40%}
{tr}
{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
{td}
{tr}
{tr}
{td}
{pagetree:root=Model Hierarchy|reverse=true}
{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 often useful in situations where the net force on an object is constant.  It is a subclass of the [One-Dimensional Motion (General)] model defined by the constraint da/dt = 0. {excerpt}

----
|| Page Contents ||
| {toc:style=none|indent=10px} |

----
h2. Assumed Knowledge

h4. Prior Models

* [1-D Motion (Constant Velocity)]

h4. Vocabulary

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

----
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.
\\
\\
{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}$\end{large}{latex}\\
\\
{latex}\begin{large}$v^{2} = v_{\rm i}^{2} + 2 a (x - x_{\rm i})$\end{large}{latex}

----
h2. Relevant Examples

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

----
{search-box}
\\
\\
| !copyright and waiver^copyrightnotice.png! | RELATE wiki by David E. Pritchard is licensed under a [Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License|http://creativecommons.org/licenses/by-nc-sa/3.0/us/]. |
\\