Class 9 Chapter: Motion - Lecture Notes

Introduction

• This is the final session on the chapter 'Motion'.
• Focus on graphs, equations of motion (kinematic equations), and related problems.
• Previous videos covered introductory concepts.

Motion Graphs

Types of Graphs

• *Distance-Time Graph (Position-Time Graph)*
  • Used to describe motion by plotting distance covered over time.
  • Examples: Cricket match run analysis.
  • Axes: X-axis (Time), Y-axis (Distance).

Distance-Time Graph for Uniform Motion

• Characteristics: Straight line indicating equal distances covered in equal intervals of time.
• Example Plot:
  • 1s => 2m
  • 2s => 4m
  • 3s => 6m
  • 4s => 8m
  • 5s => 10m
• Key Points:
  • Always consider time on the x-axis and distance on the y-axis.
  • Equal distances in equal intervals => Uniform Motion => Straight Line.

Distance-Time Graph for Non-Uniform Motion

• Characteristics: Curve indicating unequal distances covered in equal intervals of time.
• Example Plot:
  • 2s => 1m
  • 4s => 4m
  • 6s => 9m
  • 8s => 16m
  • 10s => 25m
• Key Points:
  • Unequal distances in equal intervals => Non-Uniform Motion => Curve.

Uses of Distance-Time Graph

• Speed Calculation: Distance/Time.
  • E.g., at point A (Time = 2s, Distance = 4m) => Speed = 4m/2s = 2m/s.
• Velocity Calculation: Displacement/Time.
  • E.g., between points A and B (Distance A = 4m, Distance B = 8m, Time = 2s) => Velocity = (8m-4m)/(4s-2s) = 2m/s.

Velocity-Time Graph

Vt Graph for Uniform Motion

• Characteristics: Straight line parallel to the x-axis indicating constant velocity.
• Example Plot:
  • 1s => 20m/s
  • 2s => 20m/s
  • 3s => 20m/s
  • 4s => 20m/s
• Key Points: Constant velocity implies Uniform Motion.

Vt Graph for Non-Uniform Motion

• Characteristics: Inclined straight line indicating uniformly accelerated motion.
• Example Plot:
  • As time increases, velocity increases linearly.
• Key Points: Non-Uniform Motion with Uniform Acceleration => Straight Line.

Uses of Velocity-Time Graph

• Displacement Calculation: Area under the Vt graph.
  • Area of rectangle: Length x Breadth.
  • Area of trapezium: (1/2) x (Sum of parallel sides) x (Height).

Important Equations of Motion

First Equation: v = u + at

• Derivation: Using Vt graph.
  • Initial velocity (u), final velocity (v), time (t), acceleration (a).
  • Derived from the definition of acceleration (change in velocity over time).

Second Equation: s = ut + 1/2 at²

• Derivation: Using area under Vt graph.
  • Distance (s), initial velocity (u), time (t), acceleration (a).
  • Area of triangle + area of rectangle.

Third Equation: v² - u² = 2as

• Derivation: Using average velocity and basic definitions.
  • Derived from average velocity (v + u)/2 and displacement (s).

Solved Examples

Example 1: Train Motion

• Given:
  • Initial velocity (u) = 0 m/s
  • Final velocity (v) = 72 km/h = 20 m/s
  • Time (t) = 5 minutes = 300 seconds
• Find Acceleration (a):
  • Using v = u + at
  • a = (v - u) / t = (20 - 0) / 300 = 1/15 m/s²
• Find Distance (s):
  • Using s = ut + 1/2 at²
  • s = 0 + 1/2 * 1/15 * 300² = 3000 meters = 3 kilometers

Example 2: Car Braking

• Given:
  • Final velocity (v) = 0
  • Acceleration (a) = -6 m/s²
  • Time (t) = 2 seconds
• Initial velocity (u) calculation:
  • Using v = u + at
  • u = v - at = 0 - (-6 * 2) = 12 m/s
• Find Distance (s):
  • Using s = ut + 1/2 at²
  • s = 12 * 2 + 1/2 * (-6) * 2² = 12 meters

Conclusion

• Understanding motion graphs and equations is crucial.
• Practice problems to master the concepts.
• Stay tuned for the next chapter.