Section 1 of 9Two ways to describe a journey
| Feature | Distance | Displacement |
|---|---|---|
| Meaning | How far an object has moved along its path | How far the object is from its start, in a straight line, with direction |
| Type of quantity | Scalar - magnitude only | Vector - magnitude and direction |
| Can it be zero after a journey? | No, if the object has moved | Yes, if it returns to the start |
| Example | 30 m | 30 m north |
| Unit | Metre (m) | Metre (m), with a direction |
Section 2 of 9Scalars and vectors
Two kinds of quantity
Scalar
- Scalar A scalar has only a size. Distance, speed, mass and time are scalars.
Vector
- Vector A vector has size and direction. Displacement, velocity, force and acceleration are vectors.
Direction in calculations
- Direction in calculations Direction is often shown by a plus or minus sign, with one way chosen as positive.
Section 3 of 9Worked idea: a 300 m race
1Runners start
- Runners start The runners begin at the start line on a 400 m track.
2Distance covered
- Distance covered After running 300 m around the track, the distance travelled is 300 m.
3Displacement
- Displacement The runners finish 100 m short of the start line, so their displacement is 100 m in the direction of the start from where they stopped.
4Full lap
- Full lap After the full 400 m the distance is 400 m but the displacement is zero.
Section 4 of 9Finding displacement
1
Mark the starting point and the finishing point of the movement.
2
Draw a straight line from start to finish, ignoring the path actually taken.
3
Measure or calculate the length of this line; this is the size of the displacement.
4
State the direction, such as east, or a positive or negative sign.
5
Compare with the distance, which is the length of the full path followed.
Section 5 of 9Worked examples: distance and displacement
| Journey | Distance | Displacement |
|---|---|---|
| Walk 40 m east, then 30 m north | 70 m | 50 m on a bearing of about 053 degrees (use Pythagoras: 402 + 302 = 502) |
| Walk 20 m east, then 20 m west | 40 m | 0 m, because you finish where you began |
| One lap of a 400 m running track | 400 m | 0 m |
| A lift rises 12 m, then falls 5 m | 17 m | 7 m upwards |
| A ball is thrown up 8 m and caught at the same point | 16 m | 0 m |
Section 6 of 9Where the idea is used
Navigation
- Navigation Pilots, sailors and satellite navigation systems work with displacement,
- because they need to know both how far away a destination is and in which direction to head.
Later topics
- Later topics Velocity and acceleration are defined using displacement,
- so being clear about the difference now makes later motion calculations much easier.
Graphs
- Graphs On a displacement-time graph the line can go downwards if the object moves back towards the start, but a distance-time graph can never fall.
Section 7 of 9Exam approach
Distance or displacement?
Look for the key word
- Look for the key word If the question says how far an object has travelled or the total path, give a distance.
- If it asks how far from the start, or in which direction, give a displacement.
Sketch the journey
- Sketch the journey A quick diagram with arrows for each stage shows whether the object doubles back, which is when distance and displacement differ.
Always add direction
- Always add direction A displacement answer is incomplete without a direction such as 7 m upwards, 50 m north-east or a plus or minus sign.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Distance | The total length of the path travelled by an object; a scalar quantity. |
| Displacement | The straight-line distance from start to finish together with its direction; a vector. |
| Scalar | A quantity with magnitude only. |
| Vector | A quantity with both magnitude and direction. |
| Magnitude | The size of a quantity. |
Section 9 of 9Exam technique
1
Giving displacement without a direction.
2
Assuming distance and displacement are always equal; they match only for straight-line motion in one direction.
3
Measuring displacement along the curved path rather than in a straight line from start to finish.
4
Saying the displacement is the distance when a runner finishes at their start point; it is zero.