Understanding Distance, Displacement, Speed, and Velocity

Oct 2, 2024

Kinematics: Distance, Displacement, Speed, and Velocity

Introduction

  • Focus on distance, displacement, speed, and velocity.
  • Unique concepts to aid understanding.

Distance vs. Displacement

Definitions

  • Distance: Total path covered by a body in a given time.
    • Denoted by: s, x, m, etc.
    • SI unit: meter (m)
  • Displacement: Shortest and directed path traveled by a body.
    • Denoted by: s arrow, x arrow, rm arrow.
    • SI unit: meter (m)

Key Differences

  • Distance is a scalar quantity (no direction).
  • Displacement is a vector quantity (includes direction).

Example

  • Road 1 (Distance): 100 meters (s = 100 m)
  • Road 2 (Displacement): 70 meters (s arrow = 70 m)

Why the Difference?

  • Distance changes direction constantly (Road 1).
  • Displacement maintains a constant direction (Road 2).

Speed vs. Velocity

Definitions

  • Speed: Rate at which an object covers distance.
    • Formula: Speed (v) = Distance (s) / Time (t)
    • SI unit: meter per second (m/s)
    • Scalar quantity.
  • Velocity: Rate at which an object covers displacement.
    • Formula: Velocity (v arrow) = Displacement (s arrow) / Time (t)
    • SI unit: meter per second (m/s), with direction.
    • Vector quantity.

Importance of Velocity

  • Speed shows how fast an object is moving.
  • Velocity indicates speed and direction of motion.
    • Example:
      • Speed: 30 m/s
      • Velocity: 30 m/s towards the right.

Numerical Problems

Perimeter of Shapes

  • Perimeter = Length of a boundary of any shape.
    • Circle: 2πr
    • Rectangle: 2(l + b)
    • Triangle: a + b + c

Example Problem: Walking Around a Circle

  1. Distance: Total length walked (2πr).
  2. Displacement: Zero if initial and final positions are the same.
  3. Speed: Distance / Time.
  4. Velocity: Displacement / Time.

Example Problem: Car Traveling from P to Q

  • Distance = Perimeter of semi-circle (πr).
  • Speed = Distance / Time.
  • Displacement = Diameter of the circle (2r).
  • Velocity = Displacement / Time.

Example Problem: Ball Displacement

  1. Displacement using Pythagorean theorem (hypotenuse = √(base² + perpendicular²)).
  2. Velocity = Displacement / Time.

Conclusion

  • Understanding of distance, displacement, speed, and velocity is crucial for solving kinematic problems.
  • Use examples to clarify concepts and calculations.