One-Dimensional Motion (General)

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 that is not sinusoidal. 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).

Prerequisite Knowledge

Prior Models

• 1-D Motion (Constant Velocity)
• 1-D Motion (Constant Acceleration)

Vocabulary

• [position (one-dimensional)]
• velocity
• acceleration

System

A single point particle (or a system treated as a point particle with position specified by the center of mass).

Interactions

Some time-varying external influence that is confined to one dimension.

Model

Laws of Change

Diagrammatic Representations

• Acceleration versus time graph.
• Velocity versus time graph.
• Position versus time graph.

Relevant Examples

None yet.