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h2. Description
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*Hierarchy of Models* {td}{tr}{tr}{td}
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This model applies to a point particle subject to an external force that is either parallel or antiparallel to the particle's initial velocity.  {excerpt}

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h2. Assumptions and Limitations


h4. Prior Models

* Link to model pages that should be learned before this model.

h4. Vocabulary

* [frame of reference]
* [position (one-dimensional)]
* [velocity (one-dimensional)]
* [acceleration (one-dimensional)]

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h2. Model Specification


h4. *System Structure*


h4.  

*Internal Constituents:* Point particle.

*Environment:* external agents interacting with the particle which are the responsible of the *real* forces acting *on* the particle. The total external force must be parallel or anti-parallel to the paticle's initial velocity.

h4. Descriptors

*Object Variables:* none

*State Variables:* Time (_t_), position (_x_) , and velocity (_v_).

*Interaction Variables:* acceleration _a_.

h4. Laws of Interaction

Any external force which magnitude is not constant. Possible forces are forces that depends on time, on the particle's position or on the particle's velocity.
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h4. Laws of Change

integral formdifferential form{latex}$\vec v${latex} 
 
{latex}\begin {large}$x(t_f) = x(t_i) + \int_{t_i}^{t_f} v(t)dt  v(t) = \frac{dx(t)}{dt} $ \end{large}{latex}

 
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{latex}\begin {large}$v(t_f) = v(t_i) +\int_{t_i}^{t_f} a(t)dt v(t) =\frac{dv(t)}{dt}$ \end{large}{latex}
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h2. Relevant Examples

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{contentbylabel:1d_motion,constant_acceleration,example_problem\|showSpace=false\|showLabels=false\|maxResults=50}

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