Description and Assumptions
This model is applicable to a single point particle subject to an acceleration that is constrained to one dimension and which is either parallel to or anti-parallel to the particle's initial velocity.
Problem Cues
In practice, this model is only useful when a one-dimensional acceleration is given that has a known time dependence. If the acceleration is constant, the sub-model One-Dimensional Motion with Constant Acceleration should be used. If the acceleration is sinusoidal (described by a sine, cosine, or sum of the two), the sub-model Simple Harmonic Motion should be used. Thus, in practice, the problem cue for this model is that the acceleration will be given as an explicit and integrable function of time, most often a polynomial (the acceleration might also be plotted as a linear function of time).
Model
Compatible Systems">Compatible Systems
A single point particle (or a system treated as a point particle with position specified by the center of mass).
Relevant Interactions">Relevant Interactions
Some time-varying external influence that is confined to one dimension.
Laws of Change">Laws of Change
Diagrammatic Representations">Diagrammatic Representations
These graphs show the position, velocity , and acceleration for the motion of a particle for which the equation of motion is
\begin
[x = -0.1t^
-t^
+ 30t -100 ]\end
|
Consequently the velocity, which is the derivative of the position with respect to time, is given by
\begin
[x = -0.3t^
-2t + 30 ]\end
|
and the acceleration is given by the second derivative of the position with respect to time:
\begin
[x = -0.6t -2 ]\end
|
