Distance and displacement (AQA GCSE Physics): Revision Notes
Distance and displacement
What are distance and displacement?
Distance and displacement are both ways to measure how far an object has travelled. However, they are completely different concepts that you need to understand clearly.
Distance tells us the total path an object has taken. It doesn't matter which direction the object went - we just add up all the distances travelled.
Displacement tells us the straight-line distance from the starting point to the finishing point, plus the direction of that straight line.
Understanding distance
Distance measures how far an object travels in total. It only has a magnitude (size) and no direction. This makes distance a scalar quantity.
Key points about distance:
- Always positive (you can't travel a negative distance)
- Measures the actual path taken
- No direction needed
- Examples: 20mm, 150cm, 10m, 500km
Distance example
Worked Example: Rectangular Route Distance
Imagine a person walks around a rectangular route. They start at point A, visit points B, C and D, then return to A. If each side of the rectangle is different lengths, we add up all the distances:
- Total distance = all sides added together
- This gives us the complete journey length
- Direction doesn't matter for distance
Understanding displacement
Displacement measures the straight-line distance from start to finish, including the direction travelled. It has both magnitude and direction. This makes displacement a vector quantity.
Key points about displacement:
- Can be positive, negative, or zero
- Measures the direct route from start to finish
- Always includes direction
- Examples: 20mm to the left, 10m North, 500km on a bearing of 90°
Displacement example
Worked Example: Rectangular Route Displacement
Using the same rectangular route, if the person starts at point A and returns to point A:
- Total displacement = 0km
- This is because they ended up back where they started
- The direction doesn't apply when displacement is zero
However, if they stopped at a different point, the displacement would be the straight-line distance from A to that point, with a direction.
Worked example - calculating both
Worked Example: Baby Crawling Problem
The problem: A baby crawls 3m from her cot at point A, turns 90° at point B, then crawls another 4m to point C.
Finding distance:
- Distance =
- We simply add up all the distances travelled
Finding displacement:
- The baby has moved in a straight line from A to C
- Using Pythagoras' theorem: displacement = from A
- Direction can be found using trigonometry (bearing of 53° from North)
Key differences
| Distance | Displacement |
|---|---|
| Scalar quantity | Vector quantity |
| Total path travelled | Straight line from start to finish |
| Always positive | Can be positive, negative or zero |
| No direction needed | Always includes direction |
| Longer or equal to displacement | Shorter or equal to distance |
Critical Concepts to Avoid Confusion:
- If you travel in a straight line, distance and displacement are equal
- If you return to your starting point, displacement is zero but distance is not
- Displacement can never be greater than distance
- Direction is crucial for displacement - use bearings, compass points, or left/right
Key Points to Remember:
- Distance = total journey length (scalar)
- Displacement = straight line from start to finish with direction (vector)
- Distance is always positive, displacement can be zero if you return to start
- Add up all distances for total distance
- Use Pythagoras' theorem to find displacement in right-angled situations