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| System: One point particle constrained to move in one dimension. — Interactions: Any that respect the one-dimensional motion. |
Introduction to the ModelDescription and AssumptionsThis 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 ObjectivesStudents 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 ModelCompatible SystemsA single point particle (or a system treated as a point particle with position specified by the center of mass). Relevant InteractionsSome time-varying external influence that is confined to one dimension. Laws of ChangeMathematical Representation| Section |
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\begin{large}\[ \frac{dv}{dt} = a\]\end{large} |
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\begin{large}\[ \frac{dx}{dt} = v\]\end{large} |
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\begin{large}\[ v(t) = v(t_{i})+\int_{t_{i}}^{t} a\;dt\]\end{large} |
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\begin{large}\[ x(t) = x(t_{i})+\int_{t_{i}}^{t} v\;dt\]\end{large} |
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Diagrammatic RepresentationsRelevant Examples All Examples Relevant to the Model | Content by Label |
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| example_problem,nonuniform_acceleration |
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| example_problem,nonuniform_acceleration |
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| showLabels | true |
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| maxResults | 50 |
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| showSpace | false |
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| excerpt | true |
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| operator | AND |
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| excerptType | simple |
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| cql | label = "nonuniform_acceleration" and label = "example_problem" |
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