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

Compare with Current View Page History

« Previous Version 58 Next »

Unknown macro: {table}
Unknown macro: {tr}
Unknown macro: {td}

Description and Assumptions

This model is applicable to a single point particle subject to an acceleration that is constrained to one dimension and which is either parallel to or anti-parallel to the particle's initial velocity.

Problem Cues

In practice, this model is only useful when a one-dimensional acceleration is given that has a known time dependence. If the acceleration is constant, the sub-model One-Dimensional Motion with Constant Acceleration should be used. If the acceleration is sinusoidal (described by a sine, cosine, or sum of the two), the sub-model Simple Harmonic Motion should be used. Thus, in practice, the problem cue for this model is that the acceleration will be given as an explicit and integrable function of time, most often a polynomial (the acceleration might also be plotted as a linear function of time).

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

Some time-varying external influence that is confined to one dimension.

Laws of Change

Differential Forms
Unknown macro: {latex}

\begin

Unknown macro: {large}

[ \frac

Unknown macro: {dv}
Unknown macro: {dt}

= a]\end



Unknown macro: {latex}

\begin

Unknown macro: {large}

[ \frac

Unknown macro: {dx}
Unknown macro: {dt}

= v]\end



Integral Forms
Unknown macro: {latex}

\begin

Unknown macro: {large}

[ v(t) = v(t_

Unknown macro: {i}

)+\int_{t_{i}}^

Unknown macro: {t}

a\;dt]\end



Unknown macro: {latex}

\begin

Unknown macro: {large}

[ x(t) = x(t_

Unknown macro: {i}

)+\int_{t_{i}}^

Unknown macro: {t}

v\;dt]\end


Diagrammatic Representations

[Click here to run a simulation demonstrating position, \\velocity and acceleration graphs for general 1-D motion|^moving-man_en.jar]

Simulation provided by:
PhET Interative Simulations
University of Colorado
[http://phet.colorado.edu]

Relevant Examples

  • No labels