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Introduction to the Model
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.
Learning Objectives
Students will be assumed to understand this model who can:
- Choose the one graph possible velocity or acceleration vs. time graphs which corresponds to a model position versus time graph.
- Differentiate position given as a polynomial function of time to find the corresponding velocity and acceleration.
- Integrate the velocity or acceleration when given as a polynomial function of time along with appropriate initial conditions to find the functional form of the position.
S.I.M. Structure of the 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
Mathematical Representation
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
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Click here to run a simulation demonstrating position,
velocity and acceleration graphs for general 1-D motion |
Simulation provided by:
PhET Interative Simulations
University of Colorado
http://phet.colorado.edu |
Relevant Examples
All Examples Relevant to the Model
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