Description
This model applies for a point particle subject to a constant acceleration that is either parallel to or antiparallel 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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Prerequisite Vocabulary
- [position (one-dimensional)]
- [velocity (one-dimensional)]
- [acceleration (one-dimensional)]
Model Specification
System Schema
Internal Constituents: None. Object must be treated as a point particle.
External Agents: Some constant external influence must be present which produces the acceleration.
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