One-Dimensional Motion (General)

Description

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Hierarchy of Models

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This model applies to a point particle subject to an external force that is either parallel or antiparallel to the particle's initial velocity.

Page Contents
Description Assumptions and Limitations Prior Models Vocabulary Model Specification System Structure Descriptors Laws of Interaction Laws of Change Relevant Examples

Assumptions and Limitations

Prior Models

Link to model pages that should be learned before this model.

Vocabulary

[frame of reference]
[position (one-dimensional)]
[velocity (one-dimensional)]
[acceleration (one-dimensional)]

Model Specification

System Structure

Internal Constituents: Point particle.

Environment: external agents interacting with the particle which are the responsible of the real forces acting on the particle. The total external force must be parallel or anti-parallel to the paticle's initial velocity.

Descriptors

Object Variables: none

State Variables: Time (t), position (x) , and velocity (v).

Interaction Variables: acceleration a.

Laws of Interaction

Any external force which magnitude is not constant. Possible forces are forces that depends on time, on the particle's position or on the particle's velocity.

Laws of Change

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\begin

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$x(t_f) = x(t_i) + \int_

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^

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v(t)dt v(t) = \frac

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$ \end

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\begin

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$v(t_f) = v(t_i) +\int_

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^

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a(t)dt v(t) =\frac

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