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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

\begin{large}\[ \frac{dv}{dt} = a\]\end{large}

\begin{large}\[ \frac{dx}{dt} = v\]\end{large}

\begin{large}\[ v(t) = v(t_{i})+\int_{t_{i}}^{t} a\;dt\]\end{large}

\begin{large}\[ x(t) = x(t_{i})+\int_{t_{i}}^{t} v\;dt\]\end{large}

Diagrammatic Representations

• position versus time graph
• velocity versus time graph
• acceleration versus time graph
• motion diagram

Relevant Examples

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All Examples Relevant to the Model