[Model Hierarchy]
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.
Problem Cues
In practice, this model is only useful when a one-dimensional acceleration is given that has a known time dependence that is not sinusoidal. If the acceleration is constant, the sub-model One-Dimensional Motion with Constant Acceleration should be used. If the acceleration is sinusoidal (described by a sine, cosine, or sum of the two), the sub-model Simple Harmonic Motion should be used. Thus, in practice, the problem cue for this model is that the acceleration will be given as an explicit and integrable function of time, most often a polynomial (the acceleration might also be plotted as a linear function of time).
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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
Some time-varying external influence that is confined to one dimension.
Interaction Variables
Acceleration (a(t)).
Model
Laws of Change
Differential Forms:
\begin
[ \frac
= a]\end
\begin
[ \frac
= v]\end
Integral Forms:
\begin
[ v(t) = v(t_
)+\int_{t_{0}}^
a\;dt]\end
\begin
[ x(t) = x(t_
)+\int_{t_{0}}^
v\;dt]\end
Diagrammatical Representations
- Acceleration versus time graph.
- Velocity versus time graph.
- Position versus time graph.
Relevant Examples
None yet.
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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 |
