Describing Motion Around Us · Lesson 2 of 10
Distance travelled and displacement
“The path took the scenic route while displacement chose the shortcut.”
• Calculate total distance from every part of a path. • Describe displacement using magnitude and direction. • Explain why displacement depends only on initial and final positions. • Apply the inequality between distance and displacement. • Identify situations with zero displacement but non-zero distance.
Suppose a runner reaches the far end of a track and then returns part of the way. The runner’s feet have covered the outward path and part of the return path, but the final position may be quite close to the start. This difference gives us two ways of describing the same journey: the complete path and the net change in position.
Distance travelled is the total length of the actual path followed by an object.
Displacement is the net change in the position of an object between two instants, directed from the initial position toward the final position.
| Property | Distance travelled | Displacement |
|---|---|---|
| What it measures | Length of the complete path | Net change from initial to final position |
| Direction required | No | Yes |
| Can be zero after motion? | No | Yes |
| Can exceed distance? | Not applicable | Its magnitude cannot exceed distance |
| SI unit | metre | metre |
Problem
A runner moves from 0 m to 100 m and returns to 40 m. Find distance and displacement.
- 1.Break the path into two parts.
- 2.Outward distance = (100-0=100 m).
- 3.Return distance = (100-40=60 m).
- 4.Total distance = (100+60=160 m).
- 5.Displacement = final position − initial position = (40-0=+40 m).
- 6.The positive sign means the final position is 40 m in the chosen positive direction.
Activity: Let us analyse
Consider a ball thrown vertically upward from (O). It passes (A) at 40 cm, reaches (B) at 140 cm, falls past (C) at 80 cm and finally returns to (O). At every stage, add the length of each path segment to obtain distance. For displacement, subtract the starting position from the current position.
| Current position | Total distance from the start | Displacement from the start |
|---|---|---|
| O before release | 0 cm | 0 cm |
| A while rising | 40 cm | 40 cm upward |
| B at the top | 140 cm | 140 cm upward |
| C while falling | 140 cm + 60 cm = 200 cm | 80 cm upward |
| O after return | 140 cm + 140 cm = 280 cm | 0 cm |
Problem
A walker travels 60 m east and then 60 m west. Find distance and displacement.
- 1.Add the two path lengths: distance = (60+60=120 m).
- 2.The final position is the same as the initial position.
- 3.Displacement = final position − initial position = 0.
- 4.The walker moved, so distance is non-zero even though displacement is zero.
Ready to Go Beyond
A quantity described completely by a numerical value and unit is called a scalar quantity. Distance is scalar. A quantity that requires magnitude, direction and unit is called a vector quantity. Displacement is vector-like because saying “40 m” without a direction does not completely describe it.
Pause and Ponder
Fuel use is connected more closely with distance travelled because the vehicle operates throughout the complete route. Returning to the starting point does not restore the fuel merely because displacement becomes zero. This is an important reminder that different physical quantities answer different questions.
Note
For straight-line motion without reversal, distance travelled equals the magnitude of displacement. The equality fails as soon as the object turns back. On a straight inclined track, the motion can still be represented using a horizontal number line because the line represents position along the track, not its visible orientation in space.
Distance is obtained by adding the lengths of all travelled segments. Subtraction is used for net change in position.
Quiz
Which description best matches Distance Travelled?
Which description best matches Displacement?
Which term matches this description: Distance travelled is the total length of the actual path followed by an object.
Which term matches this description: Displacement is the net change in the position of an object between two instants, directed from the initial position toward the final position.
Which statement is a key takeaway from this lesson?
Practice Problems
- A person walks 70 m north and 20 m south. Find distance and displacement.
- A ball rises 15 m and returns to the release point. Find distance and displacement.
- State the condition for distance to equal displacement magnitude.
- Explain why fuel consumption is not determined by displacement.
Key Takeaways
• Distance records the complete path. • Displacement connects initial and final positions. • Displacement requires direction. • Displacement magnitude never exceeds distance. • A round trip can have zero displacement and non-zero distance.