Scalars & Vectors (Cambridge (CIE) IGCSE Physics)

Scalar & vector quantities

Extended tier only

• All quantities can be one of two types:

  • A scalar

  • A vector

Scalars

• Scalar quantities have only a magnitude

  • Mass is an example of a scalar quantity because it has magnitude without direction

  • Energy and volume are also examples of scalar quantities

Vectors

• Vector quantities have both magnitude and direction

  • Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction

  • Acceleration and momentum are also examples of vector quantities

Distance and displacement

• Distance is a measure of how far an object has travelled, regardless of direction
  

  • Distance is the total length of the path taken

  • Distance, therefore, has a magnitude but no direction

  • So, distance is a scalar quantity

• Displacement is a measure of how far it is between two points in space, including the direction
  

  • Displacement is the length and direction of a straight line drawn from the starting point to the finishing point

  • Displacement, therefore, has a magnitude and a direction

  • So, displacement is a vector quantity

What is the difference between distance and displacement?

Displacement is a vector quantity, while distance is a scalar quantity

• When a student travels to school, there will probably be a difference between the distance they travel and their displacement

  • The overall distance they travel includes the total lengths of all the roads, including any twists and turns

  • The overall displacement of the student would be a straight line between their home and school, regardless of any obstacles, such as buildings, lakes or motorways, along the way

Speed and velocity

• Speed is a measure of the distance travelled by an object per unit time, regardless of the direction

  • The speed of an object describes how fast it is moving, but not the direction it is travelling in

  • Speed, therefore, has magnitude but no direction

  • So, speed is a scalar quantity

• Velocity is a measure of the displacement of an object per unit time, including the direction

  • The velocity of an object describes how fast it is moving and which direction it is travelling in

  • An object can have a constant speed but a changing velocity if the object is changing direction

  • Velocity, therefore, has magnitude and direction

  • So, velocity is a vector quantity

Examples of scalars & vectors

Extended tier only

• The table below lists some common examples of scalar and vector quantities

• Corresponding scalars and their vector counterparts are aligned in the table where applicable

Table of scalars and vectors