Scalars vs Vectors

Scalar

• Only magnitude (single number).
• Examples:
  • Speed
  • Temperature
  • Weight

Vector

• Has magnitude and direction.
• Examples:
  • Velocity
  • Acceleration
  • Magnetic field
• Notation:
  • Often bold (v)
  • Sometimes arrow over letter ( v⃗\vec{v}v )

Distance vs Displacement

• Distance: Total path traveled (scalar)
• Displacement: Straight-line distance with direction (vector)

Example:

• Run 3 km but end 500 m south of start.
  • Distance = 3 km
  • Displacement = 500 m south

Speed and Velocity

• Speed: Scalar → distance / time
  • Example: 4 km/h
• Velocity: Vector → displacement / time
  • Example: 0.5 km/h South
• Instantaneous Velocity: Measured at a specific moment
• Average Velocity: Measured over entire journey