Scalars & Vectors
- All quantities can be one of two types:
- a scalar
- a vector
Scalars
- Scalars are quantities that have magnitude but not direction
- For example, mass is a scalar quantity because it has magnitude but no direction
Vectors
- Vectors are quantities that have both magnitude and direction
- For example, weight is a vector quantity because it is a force and has both magnitude and direction
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 in 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
- The table below lists some common examples of scalar and vector quantities
Table of scalars and vectors
| Scalars | Vectors |
| distance | displacement |
| speed | velocity |
| mass | acceleration |
| time | force |
| energy | momentum |
| volume | |
| density | |
| pressure | |
| electric charge | |
| temperature |
