Distance & Displacement

Definition of Distance

Distance is a scalar quantity, which means it only has magnitude (size) and no direction. It measures the total length of the path travelled by an object, regardless of the direction taken.

Distance is always positive or zero because it represents how much ground an object has covered. It never decreases or becomes negative.

For example, if you walk 3 metres forward, then 4 metres back, your total distance travelled is 7 metres.

Definition of Displacement

Displacement is a vector quantity, meaning it has both magnitude and direction. It is the shortest straight line from the starting point to the ending point of an object's motion.

Displacement shows how far and in which direction an object is from its starting position, not the total path length travelled.

For instance, if you walk 3 metres forward, then 4 metres back, your displacement is 1 metre backwards (since you end up 1 metre behind your starting point).

Difference Between Distance and Displacement

• Distance is scalar; it only has size. Displacement is vector; it has size and direction.
• The magnitude of displacement is always less than or equal to the distance travelled. This is because displacement is the shortest straight line between start and end points.
• Displacement can be zero if the object ends up back at its starting point, but distance will be the total length travelled (which is not zero).

For example, if a runner completes one lap of a 400 m track, the distance is 400 m but the displacement is zero because the start and end points are the same.

Representing Distance & Displacement

Displacement is often represented graphically using arrows. The length of the arrow shows the magnitude (size) of the displacement, and the arrow points in the direction of displacement.

Distance is usually shown as a numerical value without direction.

Both distance and displacement are measured in metres (m) in the SI system.

On diagrams, displacement arrows help visualise motion by showing how far and in what direction an object has moved from its starting point.

For instance, if a person walks 5 m east and then 3 m north, the displacement arrow would point diagonally from the start to the final position, showing the shortest straight-line distance and direction.

To calculate the magnitude of displacement in such cases, you can use Pythagoras’ theorem:

$$\text{Displacement} = \sqrt{(5\,\text{m})^2 + (3\,\text{m})^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83\,\text{m}$$

Example: A cyclist rides 10 m north, then 6 m south. What are the distance travelled and displacement?

Distance = 10 m + 6 m = 16 m (total path length)

Displacement = 10 m north - 6 m south = 4 m north (shortest straight line from start to end)

For example, if a person walks 3 m east and then 4 m north, the displacement is $\sqrt{3^2 + 4^2} = 5\,\text{m}$.