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Composition Setup
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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_{
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h1. One-Dimensional Motion with Constant Velocity

h4. {toggle-cloak:id=desc} Description and Assumptions

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{excerpt:hidden=true}*System:* One [point particle]. --- *Interactions:* No acceleration (zero net force).{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.
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h4. {toggle-cloak:id=cues} Problem Cues

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For pure kinematics problems, the problem will often explicitly state that the velocity is constant, or else some quantitative information will be given (e.g. a linear position versus time plot) that implies the velocity is constant.  
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h4. {toggle-cloak:id=pri} Prior Models

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None.
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h4. {toggle-cloak:id=vocab} Vocabulary

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

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h2. Model

h4. {toggle-cloak:id=sys} {color:red} System{color}

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A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).
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h4. {toggle-cloak:id=int} {color:red}Interactions{color}

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In order for the velocity to be constant, the system must be subject to no _net_ interaction.
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h4. {toggle-cloak:id=law} {color:red}Law of Change{color}

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\\
{latex}\begin{large}$x =  x_{\rm 
i} + v (t - t_{
\rm 
i})
$
\]\end{large}
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h4. {toggle-cloak:id=diag} {color:red}Diagrammatic Representations{color}

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|!position v time w constant velocity.PNG!|

If we plot position vs. time for constant velocity the result is a straight line having slope *v* and an intercept at *t = t{~}i{~}* of *v{~}i{~}* . If the velocity is positive, then the graph will rise with increasing time (as shown above). If the velocity is in the negative direction, the graph will fall with increasing time.

The intercept with the time axis will occur at *t - t{~}i{~} = -(x{~}i{~}/v* .

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h2. Relevant Examples

h4. {toggle-cloak:id=one} Examples Involving Purely One-Dimensional Motion

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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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falsetruetrueAND50constant_velocity,1d_motion,example_problem
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h4. {
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 Examples 
 
 Involving 
 
 Determining 
 
 when 
 
 Two 
 
 Objects 
 
 Meet


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falsetruetrueAND50constant_velocity,example_problem,catch-up
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h4. {
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 Examples 
 
 Involving 
 
 Projectile 
 
 Motion


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h4. {
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 All 
 
 Examples 
 
 Using 
 
 This 
 
 Model


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