Position-Time Graphs and Motion

Aug 19, 2025

Overview

This lecture covers how to analyze and interpret position versus time graphs, focusing on slope, velocity, and motion direction.

Collecting Data and Graphing

  • Track an object's position at regular time intervals to create a data table (time vs. position).
  • Graph position (y-axis) against time (x-axis) to visualize motion.

Interpreting Slope on Position vs. Time Graphs

  • The slope of each graph segment represents velocity (Δposition / Δtime).
  • Calculate slope as rise over run: (final position - initial position) / (final time - initial time).
  • Units for slope are meters per second (m/s).

Understanding Motion from Slope

  • Positive slope indicates forward motion (e.g., 15 m/s means moving forward).
  • Zero slope (flat line) indicates the object has stopped (velocity = 0 m/s).
  • Negative slope indicates backward motion (e.g., -10 m/s means moving in reverse).

Physical Meaning of Slope Values

  • Steeper slopes mean higher speed (the steeper, the faster).
  • Horizontal (zero slope) means the object is stationary.
  • The sign of the slope shows direction: positive for forward, negative for backward.

Interpreting Changes in Motion

  • A segment with a constant positive slope = moving forward at constant velocity.
  • A segment with zero slope = stopped.
  • A segment with negative slope = moving backward, with greater steepness indicating higher reverse speed.

Key Terms & Definitions

  • Position — The specific location of an object at a given time.
  • Velocity — The rate of change of position; slope of a position vs. time graph.
  • Slope — Rise over run; on these graphs, it represents velocity.
  • Steepness — Indicates speed; steeper = faster.
  • Zero Slope — Represents no movement (object is stopped).

Action Items / Next Steps

  • Practice calculating slopes for each segment of a position vs. time graph.
  • Write out the physical meaning for each slope value in new examples.
  • Review and understand the connection between slope steepness, velocity, and motion direction.