NCERT Solutions for Class 9th Science Chapter 4 Pause and Ponder — Distance travelled and displacement

Book page 51 Updated on2026-09-08

Q1.

In the example of an athlete running back and forth on a straight track (Fig. 4.4), when will the displacement of the athlete be zero? What will be the total distance travelled in that case?

Answer

The displacement is zero the moment she comes back to her starting point O — because displacement is the net change in position, and her final position is then the same as her initial position.

displacement = final position − initial position
= 0 m − 0 m = 0 m

If she runs from O all the way to A (100 m) and returns to O, then

total distance travelled = OA + AO
= 100 m + 100 m = 200 m

Why it happens: the two quantities answer different questions. "How far did you walk?" adds every metre of the path — the return trip counts again. "Where are you now, compared with where you began?" ignores the path entirely. So a closed trip always gives zero displacement and a non-zero distance.

Check it yourself: her displacement is zero for any round trip that ends at O — O to B and back gives 0 m displacement with 80 m of distance, and O to A to O to A to O gives 0 m displacement with 400 m of distance.

Q2.

Fuel used up in a vehicle depends on which of the following? Justify your answer. (i) Total distance travelled (ii) Displacement

Answer

(i) Total distance travelled.

Why it happens: the engine has to keep pushing the vehicle against friction and air resistance over every single metre of the road it actually covers. That work — and therefore the fuel burnt — piles up along the whole path. Displacement carries no information about the path at all.

A quick test settles it. Suppose an auto-rickshaw picks you up from home, drops you at school 4 km away, and drives back home:

total distance travelled = 4 km + 4 km = 8 km
displacement = 0 km

If fuel depended on displacement, the return journey would have to be free — and the tank would be as full at the end as at the start. It clearly is not. The fuel gauge and the odometer both track distance, not displacement.

Did you know? This is exactly why an auto or taxi meter runs on the odometer reading (distance), never on how far you ended up from where you started.

Q3.

A ball rolls down an inclined track as shown in Fig. 4.6. Is its motion, a straight line motion? Assuming the starting point of the ball (O) to be the origin, can its motion from O to D be depicted using a horizontal line as shown in Fig. 4.3? Are the values of total distance travelled and magnitude of displacement from O equal or different at positions A, B, C and D?

Answer

Yes, it is straight-line motion. The track in Fig. 4.6 is a straight (though sloping) line, and the ball stays on it throughout — so the path is a straight line.

Yes, it can be shown on a line like Fig. 4.3. The motion is one-dimensional: one number (the distance along the track from O) fixes the ball's position completely. Drawing that number line horizontally on paper is only a convenience — the line stands for the track itself, and the positive direction along it is "down the slope from O towards D", not "horizontally to the right".

Reading the markings of Fig. 4.6 along the track: OA = 40 cm, AB = 10 cm, BC = 20 cm, CD = 30 cm. So the positions measured from O are

Position	Total distance travelled from O	Magnitude of displacement from O	Equal?
A	40 cm	40 cm	Yes
B	40 + 10 = 50 cm	50 cm	Yes
C	50 + 20 = 70 cm	70 cm	Yes
D	70 + 30 = 100 cm	100 cm	Yes

So at A, B, C and D the two are equal.

Why it happens: the ball moves down the incline in one direction only and never rolls back up. With no reversal, the path is the straight line joining the two positions, so its length equals the straight-line gap. The direction of the displacement, however, is along the incline — pointing down the slope — and not horizontal.

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