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š¬ Two different numbers
An athlete runs out and partly back. How far did she travel — and how far is she from where she started? These are not the same thing.
Distance travelled vs displacement — what is the difference?
How does distance differ from displacement?
A journey
Measured two ways
1. Distance travelled
Whole path, value only
Example:
Runs 160 m in all
2. Displacement
Net change + direction
Example:
40 m from the start
- An athlete runs O→A (100 m) then back A→B (60 m). The total distance travelled = OA + AB = 100 m + 60 m = 160 m .
- The straight gap between start and stop is OB = 40 m — different from the distance travelled.
- Displacement is the net change in position between two instants. It has a magnitude (the straight distance between the two positions) and a direction (from the first position towards the second).
- Distance travelled needs only a numerical value; displacement needs value and direction. SI unit of both is the metre (m) .
Distance travelled
Displacement
Total length of the actual path covered.
Net change in position between two instants.
Has only a numerical value (no direction).
Has magnitude
and
direction.
Is always positive (or zero) and never decreases.
Can be zero even after moving (if the object returns).
Equal to displacement only for one-direction motion.
Magnitude is less than or equal to the distance travelled.
Important Definitions
- Distance travelled — the total length of the path covered by an object between the starting and stopping positions.
- Displacement — the net change in the position of an object between two given instants of time.
- Magnitude — the numerical value (with units) of a physical quantity; the magnitude of displacement is the straight distance between the object’s positions at the two instants.
š¹ Ready to Go Beyond — scalars and vectors
- Physical quantities that can be specified by just their numerical value are called scalars (e.g. distance, speed).
- Physical quantities that require both direction and magnitude are called vectors (e.g. displacement, velocity). You will learn more about these in higher grades.
Scalar
Vector
Specified by a numerical value (with units) only.
Specified by both magnitude and direction.
Examples: distance travelled, speed.
Examples: displacement, velocity, acceleration.
In this Activity, we will track a ball thrown straight up from O to the top and back, recording its distance travelled and displacement at each position to compare the two quantities.
The motion
- A ball is thrown vertically up from O, rises to the top B, then falls back to O. This is a motion in a straight line (up and down along the same vertical line).
- Fill in Table 4.1 for the marked positions, then decide which statement about displacement is true.
| S. No. | Position | Total distance travelled by the ball from O till that position | Displacement of the ball from O till that position |
|---|---|---|---|
| 1. | O | 0 cm | 0 cm |
| 2. | A | 40 cm | 40 cm in upward direction |
| 3. | B | 140 cm | 140 cm in upward direction |
| 4. | C | 200 cm | 80 cm in upward direction |
| 5. | O | 280 cm | 0 cm |
Conclusion (Q3 of the activity)
- Correct option: (iii) the magnitude of displacement is less than or equal to the total distance travelled.
- They are equal only when the object moves in one direction without turning back.
ā Note
- For motion in a straight line, the total distance travelled and the magnitude of displacement are equal if the object moves in one direction (without turning back).
ā Note
- An instant of time is a single reading of the clock at a given point of time.
- A time interval is the duration between two instants of time, i.e. between two readings of a clock.
āøā¶ Pause and Ponder
- 1. When is the athlete’s displacement zero? When she returns to the starting point O. The total distance travelled is then non-zero (the whole path length she covered).
- 2. Does fuel used depend on distance or displacement? On the total distance travelled — fuel is consumed along the actual path the vehicle covers, not on the straight gap between start and end.
- 3. Ball on an inclined track (Fig. 4.6): Yes, it is straight-line motion (along the incline), so it can be shown on a single horizontal line. Since the ball moves in one direction without turning back, the total distance travelled and the magnitude of displacement from O are equal at A, B, C and D.
NCERT Question 1 — My father went to a
My father went to a shop from home which is located at a distance of 250 m on a straight road. On reaching there, he discovered that he forgot to carry a cloth bag. He came home to take it, went to the shop again, bought provisions and came back home. How much was the total distance travelled by him? What was his displacement from home?
NCERT Question 2 — A student runs from the
A student runs from the ground floor to the fourth floor of a school building to collect a book and then comes down to their classroom on the second floor. If the height of each floor is 3 m, find: (i) the total vertical distance travelled, and (ii) their displacement from the starting point.
