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h1. One-Dimensional Motion with Constant Velocity


h4. Description and Assumptions

{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, i.e. with no net force.  It is a subclass of the [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)] model defined by the constraint _a_ = 0.

h4. Problem Cues

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. Alternatively, there may be no net force on the particle, e.g. if it slides on ice or on wheels.


h4. Learning Objectives

Students will be assumed to understand this model who can:

* Describe the difference between [distance] and [displacement].
* Define average [velocity] and average [speed].
* Describe the features of a [motion diagram] that exhibits motion with constant [velocity].
* Relate [displacement], time and [velocity].
* Find [velocity] from the slope of a [position versus time graph].
* Describe the properties of the [position versus time graph] given the [velocity] and the initial [position] for a trip made at constant velocity.
* Mathematically determine when two objects moving with constant velocity will meet by constructing and solving a system of equations.
* Graphically determine when two objects moving with constant velocity will meet.


h1. Model


h4. System

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).

h4. Interactions

In order for the velocity to be constant, the system must be subject to no _net_ force.

h4. Law of Change

{latex}\begin{large}$x =  x_{\rm i} + v (t - t_{\rm i})$\end{large}{latex}\\

h4. Diagrammatic Representations

|* !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 descend with increasing time.

The intercept with the time axis will occur at *t - t{*}{*}{~}i{~}* *= \-(x{*}{*}{~}i{~}{*}*/v)* .[motion diagram]
* [position versus time graph]
* [velocity versus time graph]


h1. Relevant Examples


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

{cloak:id=one}
{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

{cloak:id=catch}
{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

{cloak:id=proj}
{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

{cloak:id=all}
{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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