Kinematics: Motion in One Dimension

Introduction

• Kinematics is the mathematics of motion.
• It includes:
  • Motion
  • Position
  • Displacement
  • Speed
  • Velocity
  • Description of speed
  • Jerk

Meaning of Dimension

• One Dimension: Motion in a straight line
• Two Dimensions: Like circular motion
• Three Dimensions: Free movement of gas molecules

Important Variables

1. Distance: A scalar quantity
2. Displacement: A vector quantity
3. Speed: A scalar quantity
4. Velocity: A vector quantity
5. Acceleration: A vector quantity
6. Jerk: Rate of change of acceleration

Distance and Displacement

• Distance: The total length of the journey from one point to another point
• Displacement: The shortest distance between the starting and ending points
  • Example:
    • Path from A to B: Two options, but displacement is the shortest path

Questions and Solutions

• Distance and Displacement for Semi-circle Travel:
  • Distance = πr
  • Displacement = 2r
• Displacement of a Mosquito in a Cube:
  • √3a (finding the body diagonal)
• Segment of a Circle:
  • 90-degree travel displacement = √2r

Speed and Velocity

Speed:

• A scalar quantity
• Formula:
  • Average Speed = Total Distance / Total Time

Velocity:

• A vector quantity
• Formula:
  • Average Velocity = Total Displacement / Total Time

Average Speed vs. Average Velocity

• In uniform motion: Both can be equal
• In different paths: Average speed is always greater than or equal to average velocity

Solve the Questions

1. A boy goes three meters east and then two meters west, what will be his average speed and velocity?
2. A person goes from A to B and returns back to A, his average velocity is 0.
3. A person walks half the distance at speed V and the other half at speed V2, find his average speed.

Summary

• Calculating distance, displacement, speed, and velocity is crucial in kinematics.
• Solving problems clarifies these concepts.

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