Description
[Model Hierarchy]
This model is applicable to a point particle subject to a constant acceleration that is either parallel to or anti-parallel to the particle's initial velocity. 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
Key to Applicablity
Object moves with uniform or constant acceleration, graph of v(t) is linear or x(t) is quadratic. Object has constant net force applied, for instance from gravity.
System Structure
Internal Constituents: Point particle.
Environment: 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
Object Variables: None.
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).
Laws of Interaction
Acceleration must be a constant.
Laws of Change
\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 |
