Lecture on Displacement and Distance

What is Distance?

• Definition: It is the total length of the path traversed by an object.
• Example: If a body goes 5 meters up and 5 meters down, the total distance = 10 meters.
• Characteristic: Distance always increases.

What is Displacement?

• Definition: It is the shortest distance between the initial and final points.
• Characteristic: It can increase or decrease, and it can be zero if the initial and final points are the same.

Difference between Distance and Displacement

• Distance: Scalar quantity
• Displacement: Vector quantity
• Relation: Distance >= Displacement

Examples and Problems

• Question: What would be the ratio of distance and displacement if a body completes a full rotation on a circular path?
• Answer: Distance = Circumference, Displacement = 0 (in a closed path)

Graphs and Calculations

• For Vectors: R2 = R1 + ΔR
• Displacement Calculation: ΔR = R2 - R1

Speed and Velocity

• Speed: Distance / Time
• Velocity: Displacement / Time
• Average Speed: Total distance / Total time
• Average Velocity: Total displacement / Total time

Acceleration

• Definition: It is the rate of change of velocity.
• Sign Convention:
  • Positive when velocity is increasing
  • Negative when velocity is decreasing

Displacement and Distance in Graphs

• Displacement-Time Graph:
  • Slope = Velocity
  • Constant slope = Uniform velocity
• Velocity-Time Graph:
  • Slope = Acceleration
  • Area = Displacement

Special Situations

• Closed Path: Displacement = 0
• Circular Path Half Rotation: Displacement = Diameter