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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}{latex}\\
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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{~}* Position versus time graph . 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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{contentbylabel:constant_velocity,1d_motion,example_problem|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
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h4. {toggle-cloak:id=catch} Examples Involving Determining when Two Objects Meet

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{contentbylabel:constant_velocity,example_problem,catch-up|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
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h4. {toggle-cloak:id=proj} Examples Involving Projectile Motion

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{contentbylabel:projectile_motion,example_problem|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50}
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h4. {toggle-cloak:id=all} All Examples Using This Model

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