One-Dimensional Motion (General)

Introduction to the Model

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.

Learning Objectives

Students will be assumed to understand this model who can:

• Choose the one graph possible velocity or acceleration vs. time graphs which corresponds to a model position versus time graph.
• Differentiate position given as a polynomial function of time to find the corresponding velocity and acceleration.
• Integrate the velocity or acceleration when given as a polynomial function of time along with appropriate initial conditions to find the functional form of the position.

S.I.M. Structure of the Model

Compatible Systems

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

Relevant Interactions

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

Laws of Change

Mathematical Representation

Differential Forms

Integral Forms

Diagrammatic Representations

• position versus time graph
• velocity versus time graph
• acceleration versus time graph
• motion diagram

Relevant Examples

All Examples Relevant to the Model

• Page:
  When 7000 hp Just Isn't Enough — Explore the kinematics of constant power (as opposed to constant force).

  • non-conservative_work
  • example_problem
  • 1d_motion
  • nonuniform_acceleration