Basics of Motion: Distance, Displacement, Speed, Velocity, and Acceleration

Key Concepts

Distance

• Definition: Length of the path followed between an object's initial and final positions.
• Characteristics:
  • Depends on total movement, not just start and end points.
  • Scalar quantity (magnitude only).
  • Can change direction without affecting the magnitude.

Displacement

• Definition: Change in position between initial and final positions.
• Characteristics:
  • Shortest linear distance between start and end points.
  • Vector quantity (magnitude and direction).
  • Affected by changes in direction.

Example Scenario

• A car follows a winding path:
  • Distance: Total path length.
  • Displacement: Straight line between start and end positions.
  • Direction impacts displacement, not distance.

Distance vs. Displacement

• Journey where total path is greater than straight line path:
  • Walking 2m east, then 2m west results in 4m distance, 0m displacement.

Graphical Interpretation

Distance-Time vs Position-Time Graphs

• Distance-Time Graphs: Show total path length over time.
• Position-Time Graphs: Show displacement over time, indicating direction.

Speed and Velocity

Speed

• Definition: Rate of change of position.
• Characteristics:
  • Scalar quantity (only magnitude).
  • Average speed = total distance / total time.
  • Gradient of distance-time graph.

Velocity

• Definition: Rate of change of position or displacement.
• Characteristics:
  • Vector quantity (magnitude and direction).
  • Average velocity = total displacement / total time.
  • Gradient of position-time graph.

Positive vs. Negative Velocity

• Positive velocity: Position changes in positive direction (e.g., north, east).
• Negative velocity: Position changes in negative direction (e.g., south, west).

Acceleration

Definition

• Rate of change of velocity over time.

Characteristics

• Vector quantity (can be positive or negative).
• Affects speed and direction.
• Average acceleration = change in velocity / time.

Graphical Interpretation

• Velocity-Time Graph:
  • Constant velocity: Horizontal line.
  • Constant acceleration: Sloping line.
• Position-Time Graph:
  • Acceleration shown as curves in the graph.

Scenarios

• Positive velocity and acceleration: Object speeds up.
• Negative velocity and acceleration: Object speeds up.
• Positive velocity, negative acceleration: Object slows down.
• Negative velocity, positive acceleration: Object slows down.

Uniform Circular Motion

• Object accelerates towards center of circle due to direction change, even if speed remains constant.

Summary

• Distance is a scalar measure of path length.
• Displacement is a vector measure of change in position.
• Speed and velocity are rates of change; speed is scalar, velocity is vector.
• Acceleration is a vector measure of the change in velocity.