[Model Hierarchy]
Description and Assumptions
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.
Problem Cues
For pure kinematics problems, the problem will often explicitly state that the acceleration is constant, or else some quantitative information will be given (e.g. a linear velocity versus time plot) that implies the acceleration is constant. This model is always applicable to the vertical direction in a problem that specified gravitational freefall. The model is also sometimes useful (in conjunction with Point Particle Dynamics) in dynamics problems when it is clear that the net force is constant.
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Prerequisite Knowledge
Prior Models
Vocabulary
- [position (one-dimensional)]
- [velocity (one-dimensional)]
- acceleration
System
Constituents
A single point particle (or a system treated as a point particle with position specified by the center of mass).
Variables and Parameters
Time (t), position (x) , and velocity (v).
Interactions
Relevant Types
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.
Interaction Variables
Acceleration (a).
Model
Laws of Change
This model has several mathematical realizations that involve different combinations of the 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
Diagrammatical Representations
- Velocity versus time graph.
- Position versus time graph.
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 |
