Key Concepts: Distance, Displacement, Speed, Velocity

Distance vs Displacement

• Distance (scalar): Total path length traveled, regardless of direction. Always positive or zero.
• Displacement (vector): Straight-line distance from start to finish, with direction. Can be positive, negative, or zero.

Speed vs Velocity

• Speed (scalar): Rate of change of distance. Average speed = total distance / total time.
• Velocity (vector): Rate of change of displacement. Average velocity = displacement / time.
• Instantaneous velocity: Velocity at a specific instant, found as the limit of Δx/Δt as Δt → 0.

Key Relationships

• An object moving in a circle at constant speed has changing velocity because direction changes.
• Average speed ≥ |average velocity| (equality only for straight-line, one-direction motion).
• On a position-time graph, velocity = slope of the curve.