Keys to Applicabilty
[Model Hierarchy]
Technically, 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, but its real usefulness lies in the fact that it can describe mutli-dimensional motion with constant acceleration by separate application to orthogonal directions. Thus, it can be used describe the system's motion in any situation where the net force on the system is constant (a point particle subject only to near-earth [gravity] is a common example). It is a subclass of the One-Dimensional Motion (General) model defined by the constraint da/dt = 0.
Page Contents |
|---|
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
null |
RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License |
