Distance and displacement (AQA GCSE Physics Combined Science): Revision Notes
Distance and displacement
What are distance and displacement?
Distance and displacement both tell us how far something has moved. But they're not the same thing!
This is one of the most commonly confused concepts in physics. Understanding the difference between distance and displacement is essential for mastering motion and kinematics.
Distance
Distance tells us how far an object travels in total. Think of it like counting all your steps on a journey.
- Distance only has size (magnitude)
- It doesn't care about direction
- Distance is a scalar quantity
- Examples: 20mm, 150cm, 10m, 500km
A scalar quantity has magnitude (size) only. Think of scalars like temperature, mass, or speed - they don't have a direction associated with them.
Displacement
Displacement tells us the straight-line distance from where you started to where you finished. It also tells us which direction you went.
- Displacement has both size and direction
- It's measured in a straight line from start to finish
- Displacement is a vector quantity
- Examples: 20mm to the left, 10m North, 500km on a bearing of 90°
A vector quantity has both magnitude and direction. Other examples include velocity, acceleration, and force. Vectors are often represented with arrows showing both size and direction.
Understanding the difference
The key to understanding distance and displacement is to think about the path taken versus the final position.
Measuring distance
When someone walks around a rectangular path and returns to their starting point:
- They might walk 16km in total distance
- This counts every step they took on their journey
Measuring displacement
For the same journey where someone returns to their starting point:
- Their displacement is 0km
- This is because they ended up back where they started
- The straight-line distance from start to finish is zero
Key Insight: If you return to your starting point, your total distance will be greater than zero, but your displacement will always be exactly zero. This is because displacement only cares about your final position relative to where you started.
Calculating distance and displacement
Finding total distance
Add up all the parts of the journey:
- If you walk 3m, then 4m, then 2m
- Total distance =
Finding displacement
For displacement, you need the straight-line distance and direction from start to end:
- You can use scale drawings
- You can use Pythagoras' theorem for right-angled triangles
- You can use trigonometry to find the direction
When calculating displacement, remember that you're finding the shortest path between two points - this is always a straight line, regardless of the actual path taken.
Real examples
Worked Example 1: Baby crawling
A baby crawls 3m east, turns 90°, then crawls 4m north:
Step 1: Find the total distance Total distance =
Step 2: Find the displacement using Pythagoras' theorem Since the baby moved in perpendicular directions, we have a right-angled triangle:
Step 3: Find the direction The baby is 5m from the starting point at an angle north-east.
Worked Example 2: Runner in a race
A runner goes from point A through a forest to point B:
Distance: The length of the actual path taken through the forest (e.g., 800m following the winding trail)
Displacement: The straight line from A to B (e.g., 600m due north)
The displacement is always less than or equal to the distance travelled.
Key differences
| Distance | Displacement |
|---|---|
| Total path travelled | Straight line from start to end |
| Scalar (size only) | Vector (size and direction) |
| Always positive | Can be zero |
| Doesn't depend on direction | Direction matters |
Common Mistake: Students often think distance and displacement are the same when moving in a straight line. While they have the same magnitude in this case, displacement still includes direction information, making it a vector quantity.
Key Points to Remember:
- Distance = total journey length (like your car's odometer)
- Displacement = straight line from start to finish with direction
- Distance is scalar (size only), displacement is vector (size and direction)
- If you return to your starting point, distance > 0 but displacement = 0
- Use Pythagoras' theorem to calculate displacement in right-angled situations