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Introduction to the Model
Description and Assumptions
 Excerpt
hiddentrue
System: One point particle. — Interactions: No acceleration (zero net force).
This model is applicable to a single point particle moving with constant velocity, which implies that it is subject to no net force (zero acceleration). Equivalently, the model applies to an object moving in one-dimension whose position versus time graph is linear. It is a subclass of the One-Dimensional Motion with Constant Acceleration model defined by the constraint a = 0.
Learning Objectives
Students will be assumed to understand this model who can:
S.I.M. Structure of the Model
Compatible Systems
A single point particle (or a system treated as a point particle with position specified by the center of mass).
Relevant Interactions
In order for the velocity to be constant, the system must be subject to no net force.
Law of Change
Mathematical Representation
 Latex
\begin{large}\[x(t) =  x_{i} + v 
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{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*
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h2. Description and Assumptions

{excerpt}This model is applicable to a single [point particle] moving with constant velocity.  It is a subclass of the [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)] model defined by the constraint _a_ = 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})
$\end{large}{latex}\\
\\
{latex}\begin{large}$ 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}

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h2. Diagrammatical Representations

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

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h2. Relevant Examples

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

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| !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/]. |
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Diagrammatic Representations
Image Added
Click here for a Mathematica Player application illustrating these representations.
Image Added
Click here to download the (free) Mathematica Player from Wolfram Research
Relevant Examples
 
 Toggle Cloak
idone
 Examples Involving Purely One-Dimensional Motion
 
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idone
 falsetruetrueAND50constant_velocity,1d_motion,example_problem
 
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idcatch
 Examples Involving Determining when Two Objects Meet
 
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idcatch
 falsetruetrueAND50constant_velocity,example_problem,catch-up
 
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idproj
 Examples Involving Projectile Motion
 
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idproj
 falsetruetrueAND50projectile_motion,example_problem
 
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idall
 All Examples Using This Model
 
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idall
 falsetruetrueAND501d_motion,constant_velocity,example_problem falsetruetrueAND50projectile_motion,example_problem
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