Notes on Motion Graphs

Jul 15, 2024

Lecture Notes on Motion Graphs

Introduction

  • Lecture Topic: Understanding motion graphs (Displacement-Time, Velocity-Time, Acceleration-Time).
  • Importance: Clarify confusions regarding these graphs and interpret their meanings.
  • Tools: Pen and copy suggested for notes.

Basic Definitions

  • Displacement vs. Time Graph (ST Graph): Illustrates how displacement changes over time.
  • Velocity: Change in displacement over time (slope of the Displacement vs. Time graph).
  • Slope Calculation: Slope = (y2 - y1) / (x2 - x1). In ST graph, slope represents velocity.

Displacement vs. Time Graph

Key Concepts

  • The angle with the positive x-axis in the graph indicates the slope (velocity).
  • Slope represented by tan(╬╕).
  • Steeper the angle, higher the velocity.
  • Example with cars A and B: Larger angle denotes higher velocity.

Example Problems

  1. **Simple Numerical Example: Graph with defined regions O, A, B, C:
    • O to A Region: Slope = (10 - 0) / (10 - 0) = 1 m/s.
    • A to B Region: Slope = 0 (Horizontal line means velocity = 0).
    • B to C Region: Slope = (15 - 10) / (20 - 15) = 1 m/s again.
  2. Modified Numerical Example: Different values given, students encouraged to solve similarly.
    • O to A Region: Velocity = 2 m/s.
    • A to B Region: Velocity = 0 (Horizontal).
    • B to C Region: Velocity = -1 m/s (Negative velocity, body returning to origin).

Special Cases and Observations

  • Horizontal ST graph implies zero velocity.
  • Slope of the displacement-time graph for positive or negative direction indicates motion direction (positive slope: forward motion, negative slope: backward motion).
  • **Graphs for Accelerated Motion:
    • Concave Upward: Positive acceleration.
    • Concave Downward: Negative acceleration.
  • Velocity and Acceleration Concepts:
    • Same sign indicates speeding up.
    • Opposite sign indicates slowing down.

Velocity vs. Time Graph

Key Concepts

  • Slope of the Velocity-time graph indicates acceleration (change in velocity over time).
  • Area under the graph indicates displacement.

Example Problems

  1. Simple Example: Given VT graph, determine acceleration and displacement for O to A and A to B regions.
  2. Combined Example: Interpreting both VT and ST graphs to derive complete motion status over a given period.

Acceleration vs. Time Graph

Key Concepts

  • Slope of the Acceleration-Time graph represents 'jerk' (change in acceleration over time, usually not tested).
  • Area under the curve represents change in velocity.

Example Problems

  1. Simple Example: Given AT graph, find the change in velocity using the area under the curve.

Conclusion

  • Review key learnings: Interpretation of different types of motion graphs.
  • Practical applications: Deriving velocity, acceleration, displacement from graphical data crucial for solving physics problems.
  • Recommendations: Practice with multiple graph scenarios to grasp the concept thoroughly.