Kinematics: Motion in One Dimension

Introduction to Kinematics

• Kinematics: Study of motion of objects without considering the forces causing the motion.
• Focuses on mathematical calculations of speed, velocity, acceleration, distance, displacement.

Categories in Kinematics

1. Motion in One Dimension (Linear or Rectilinear)
2. Motion in Two Dimensions (e.g., Circular Motion, Projectile Motion)
3. Motion in Three Dimensions (e.g., Random motion of gas molecules)

Core Variables in Kinematics

• Distance: Scalar quantity (no direction)
• Displacement: Vector quantity (has direction)
• Speed: Scalar quantity
• Velocity: Vector quantity
• Acceleration: Rate of change of velocity
• Jerk: Rate of change of acceleration

Motion in One Dimension

• Distance vs Displacement:
  • Distance: Path length between two points (scalar)
  • Displacement: Shortest path between two points (vector)

Examples and Problem Solving

1. Ratio of Distance to Displacement:

   • Semi-circle: Distance = πr; Displacement = 2r

2. Point in a Cube:

   • Finding displacement using coordinates and body diagonal formula: Displacement = √3a

3. Displacement in Circular Motion:

   • Example: Point from A to B on a circle with radius R, covering angle θ
   • Displacement = 2R sin(θ/2)

Exercise on Distance and Displacement

1. Bus Covering Half Distance at Different Speeds
   • Distance: Sum of all distances covered
   • Displacement: Shortest distance from initial to final position

Speed and Velocity

• Average Speed: Total distance / Total time
• Average Velocity: Total displacement / Total time
• Instantaneous Speed and Velocity:
  • Speed/Velocity at a particular instant
  • Will be covered in full in the next lecture

Problem Solving on Speed and Velocity

1. Calculations and Examples
   • Man covers distance in different segments at different speeds
2. Conceptual Understanding
   • Average speed vs Average velocity
   • Speed time and distance relationships

Average Speed Calculation Examples

1. Man Covering Equal Distances at V1 and V2

2. Equally Tour Bus Problem

Special Questions and Concept Clarification

1. Bus Covering Half Distance at Speed V and Remaining Half at V1 and V2
   • Finding average speed and average velocity using defined formulas

Speed and Velocity in Various Motions

1. General Cases in Exams

Detailed Types of Speed and Velocity

• Average vs Instantaneous:
• Formulas and calculation methods

Summary

• Engage with problems to understand concepts better
• Instantaneous speed and velocity to be covered in next lecture

Next Topic

• Detailed explanation of instantaneous speed and velocity with differentiation examples