[Model Hierarchy]
Description and Assumptions
This model is technically applicable to any point particle. In practice, however, the vector equations in this model are usually split into three one-dimensional equations, so that the One-Dimensional Motion (General) model is nearly as general, and more easily used.
Problem Cues
This model is rarely needed in introductory mechanics, and is presented principally for intellectual completeness of the hierarchy.
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Prerequisite Knowledge
Prior Models
Vocabulary
- [position (one-dimensional)]
- velocity
- acceleration
System
Constituents
A single point particle (or a system treated as a point particle with position specified by the center of mass).
State Variables
Time (t), position (x) , and velocity (v).
Interactions
Relevant Types
Any.
Interaction Variables
Acceleration (a(t)).
Model
Laws of Change
Differential Forms:
\begin
[ \frac{d\vec{v}}
= \vec
]\end
\begin
[ \frac{d\vec{x}}
= \vec
]\end
Integral Forms:
\begin
[ \vec
(t) = \vec
(t_
)+\int_{t_{0}}^
\vec
\;dt]\end
\begin
[ \vec
(t) = \vec
(t_
)+\int_{t_{0}}^
\vec
\;dt]\end
Relevant Examples
None.
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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License |
