You are viewing an old version of this page. View the current version.

Compare with Current View Page History

« Previous Version 25 Next »

Description

This model applies for a point particle subject to a constant acceleration that is either parallel to or antiparallel to the particle's initial velocity. It is a subclass of the One-Dimensional Motion (General) model defined by the constraint da/dt = 0.

Prerequisite Vocabulary

  • position (one-dimensional)
  • velocity (one-dimensional)
  • acceleration (one-dimensional)

    Model Specification

    System Schema

    Internal Constituents:  None.  Object must be treated as a point particle.
    External Agents:  Some constant external influence must be present which produces the acceleration.

    Descriptors

    Object Variables:  None.
    State Variables:  Time (t), position (x) , and velocity (v) are possible state variables.  Note that in some cases only two of the three possible state variables will be needed.
    Interaction Variables:  Acceleration (a).

    Laws of Interaction

    Acceleration must be a constant.

    Laws of Change

    Unknown macro: {latex}

    $v_

    Unknown macro: {rm f}

    =  v_

    Unknown macro: {rm i}

    + a (t_

    - t_

    Unknown macro: {rm i}

    )$


    Unknown macro: {latex}

     $ x_

    Unknown macro: {rm f}

    = x_

    Unknown macro: {rm i}

    +\frac

    Unknown macro: {1}
    Unknown macro: {2}

    (v_

    +v_

    Unknown macro: {rm i}

    )(t_

    Unknown macro: {rm f}

    - t_

    )$


    Unknown macro: {latex}

    $ x_

    Unknown macro: {rm f}

    = x_

    Unknown macro: {rm i}

    +v_

    (t_

    -t_

    Unknown macro: {rm i}

    )+ \frac

    Unknown macro: {1}
    Unknown macro: {2}

    a(t_

    Unknown macro: {rm f}

    -t_

    )^

    Unknown macro: {2}

    $


    Unknown macro: {latex}

    $v_

    Unknown macro: {rm f}

    ^

    Unknown macro: {2}

    = v_

    Unknown macro: {rm i}

    ^

    + 2 a (x_

    - x_

    Unknown macro: {rm i}

    )$


  • No labels