5.4.6 Vector & Scalar Quantities

• What are scalar quantities defined as?

  Physical quantities described by a magnitude alone.
• What is a key characteristic of scalar quantities?


  They do not have any direction associated with them.
• Give an example of a scalar quantity.


  Distance, such as 10 meters.
• What does speed measure?

  How fast an object is moving, regardless of direction.
• What is mass?


  The amount of matter in an object.
• What does temperature indicate?

  How hot or cold something is.
• What does time measure?

  The duration of an event.
• How are scalar quantities typically manipulated?

  They are added, subtracted, multiplied, and divided using ordinary arithmetic.
• What are vector quantities defined as?

  Physical quantities that have both a magnitude and a direction.
• What is a key characteristic of vector quantities?

  They are described by a numerical value, unit, and direction.
• Give an example of a vector quantity.

  Displacement, such as 50 meters east.
• What does velocity measure?

  The speed of an object in a specific direction.
• What is force?

  An interaction that changes the motion of an object, with both magnitude and direction.
• What does acceleration measure?

  The rate of change of velocity, including direction.
• How must vector quantities be represented?

  With both magnitude and direction.
• How are vector quantities combined?

  Using vector addition and subtraction methods.
• What is the graphical representation of vectors?

  • Vectors are represented as arrows.
  • Length indicates magnitude.
  • Direction of the arrow shows direction.
• What is component form in vector representation?

  • Vectors can be broken down into horizontal (x) and vertical (y) components.
  • Example: Velocity of 50 m/s at 30° north of east can be calculated using trigonometry.
• What is the head-to-tail method in vector addition?

  It involves placing the tail of one vector at the head of another to find the resultant vector.
• How is vector addition performed analytically?


  By separately adding their x and y components.
• What is the formula for the resultant vector R when adding two vectors A and B?

  R = A + B.
• How do you calculate the magnitude of the resultant vector R?

  R = √(Rx² + Ry²).
• How is the direction (angle θ) of the resultant vector calculated?

  θ = tan⁻¹(Ry/Rx).
• What is the difference between speed and velocity?

  Speed is a scalar quantity with no direction, while velocity is a vector quantity with direction.
• What is the difference between distance and displacement?

  Distance is the total path length traveled, while displacement is the straight-line distance from start to finish.
• What is an example of force?

  A push or pull of 15 Newtons to the right.
• What are the main differences between scalar and vector quantities?

  • Scalar Quantities:
  • Magnitude only (e.g., mass, temperature, time).
  • Vector Quantities:
  • Magnitude and direction (e.g., velocity, force, displacement).
• How can vector addition be performed?

  • Graphically using the head-to-tail method.
  • Analytically by adding components.
• How are vectors represented?

  • Graphically as arrows indicating magnitude and direction.
  • In component form using horizontal and vertical components.
• What is the summary of scalar and vector quantities?

  • Scalar Quantities: Magnitude only (e.g., mass, temperature, time).
  • Vector Quantities: Magnitude and direction (e.g., velocity, force, displacement).
  • Vector Addition: Can be done graphically or using components.