Scalars & Vectors (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

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

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

Scalar	Vector
distance	displacement
speed	velocity
mass	weight
	force
	acceleration
	momentum
energy
volume
density
temperature
power