Position vs. Time Graphs - Lecture Notes

Introduction

• Instructor: Mr. Anderson
• Topic: Position vs. Time Graphs
• Part One: Focus on objects with constant velocity
• Part Two: Will cover acceleration and deceleration

Objective

• Understand how to interpret and analyze position vs. time graphs.
• Learn to transition between different types of graphs:
  • Position vs. Time
  • Velocity vs. Time
  • Acceleration vs. Time

Key Concepts

• Position vs. Time Graphs:

  • Graphically represents an object's position over time.
  • Important to determine the motion of the object.

• Slope:

  • Slope of the position vs. time graph indicates velocity.
  • A positive slope indicates movement to the right; negative slope indicates movement to the left.
  • Zero slope indicates no movement.

The Moving Man Simulation

• Created by University of Colorado.
• Allows for manipulation of position, showing real-time graph changes.
• Key Observations:
  • If the man moves quickly to a position, the graph reflects a straight line.
  • The slope of this line shows whether the object is moving at a constant velocity.

Example Analysis

• Position vs. Time Example:

  • Initial Position: 0, Final Position: 6 (at time 3 seconds).
  • Velocity calculation:
    • Rise: 6 m (from 0 to 6)
    • Run: 3 s (from 0 to 3)
    • Velocity = Rise/Run = 6 m / 3 s = 2 m/s.

• Negative Velocity Example:

  • Initial Position: 6 m, Final Position: 3 m (from 5 to 8 seconds).
  • Velocity calculation:
    • Rise: -3 m (from 6 to 3)
    • Run: 3 s (from 5 to 8)
    • Velocity = -3 m / 3 s = -1 m/s.

Constructing Velocity vs. Time Graph

• Translate from position vs. time graph to velocity vs. time graph using calculated velocities.
• Example transitions:
  • From position 1 to 3: Velocity was +2 m/s.
  • From position 3 to 5: Velocity was 0 m/s (stationary).
  • From position 5 onwards: Velocity was -1 m/s (moving left).

Summary

• Slope provides direct information about velocity.
• Understanding how to analyze and derive information from graphs is crucial for solving physics problems.
• For further practice, use the Moving Man simulation or review part two of the series for additional insights on acceleration.