Keys to Applicabilty
[Model Hierarchy]
This model is applicable to a single point particle subject to a constant acceleration that is either parallel to or anti-parallel to the particle's initial velocity. It will describe the system's motion in situations where the net force on the system is constant (a point particle subject only to near-earth [gravity] is a common example). The model can be used to describe mutli-dimensional motion by separate application to orthogonal directions. It is a subclass of the One-Dimensional Motion (General) model defined by the constraint da/dt = 0.
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Assumed Knowledge
Prior Models
Vocabulary
- [position (one-dimensional)]
- [velocity (one-dimensional)]
- [acceleration (one-dimensional)]
Model Specification
System Structure
[Constituents]: Point particle (or a system treated as a point particle with position specified by the center of mass).
Interactions: Some constant external influence must be present which produces a constant acceleration that is directed parallel or anti-parallel to the particle's initial velocity.
Descriptors
[State Variables]: Time (t), position (x) , and velocity (v) are possible state variables. Note that in some cases only two of the three possible state variables will be needed.
[Interaction Variables]: Acceleration (a).
Model Equations
Mathematical Statement of the Model
This model has several mathematical realizations that involve different combinations of state variables.
\begin
$v = v_
+ a (t - t_
)$\end
\begin
$x = x_
+\frac
(v_
+v_
)(t - t_
)$\end
\begin
$ x = x_
+v_
(t-t_
)+ \frac
a(t-t_
)^
$\end
\begin
$v^
= v_
^
+ 2 a (x - x_
)$\end
Relevant Examples
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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 |
