NCERT Solutions Class 9 Science Chapter 4 In-text Questions — Describing Motion Around Us

NCERT Class 9 Science — Describing Motion Around Us, the two Pause and Ponder boxes on pages 51 and 53. All 5 questions solved.

Also here. Solutions to the end-of-chapter questions for this chapter and the activities are on their own pages.

Both boxes in this chapter are about the same distinction, approached twice: first the difference between the total distance travelled and the displacement, then the difference between average speed and average velocity that follows from it. Two definitions carry all five questions:

• Distance travelled is the whole length of the path, and it never decreases. Displacement is the net change in position, with a direction, and its magnitude is just the straight-line distance between where the object started and where it finished.
• Average speed $=\dfrac{\text{total distance travelled}}{\text{time interval}}$, while average velocity $=\dfrac{\text{displacement}}{\text{time interval}}$.

Key insight. Ask one question of every problem here: did the object ever turn back? If it did not, the distance and the magnitude of the displacement are equal, and so are the average speed and the magnitude of the average velocity. If it did, the path keeps adding up while the displacement can shrink — all the way to zero if the object comes home. Every question in both boxes is that single test applied to a different journey.

Pause and Ponder, page 51. The box that follows Section 4.1.2, on distance travelled and displacement.

Question 1

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?

Solution. In Fig. 4.4 the athlete starts at O, runs the 100 m to A, and then turns and runs back. Her displacement is measured from O to wherever she happens to be, so it shrinks as she comes back along the track.

The displacement is zero only when the net change in position is zero — that is, when she arrives back at the starting point O itself. Stopping anywhere short of O, at B for instance, leaves a displacement of 40 m.

The distance travelled, though, never shrinks: it keeps adding up. Running out to A and back to O is $100\ \text{m} + 100\ \text{m}$.

$$\text{total distance} = OA + AO = 100 + 100 = 200\ \text{m}, \qquad \text{displacement} = 0$$

Question 2

Fuel used up in a vehicle depends on which of the following? Justify your answer.

(i) Total distance travelled

(ii) Displacement

Solution. Think about what the engine is actually doing. Fuel is burned for every metre the wheels turn, whichever way the vehicle happens to be pointing. A driver who goes 10 km out and 10 km back has burned fuel for the whole 20 km, even though the car is back where it started.

That journey has a displacement of zero. If fuel depended on displacement, the return trip would have cost nothing — which is plainly false. So the fuel used depends on the total distance travelled.

Question 3

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?

Solution. Take the three parts in turn.

Is it straight-line motion? Yes. The track in Fig. 4.6 is a straight, sloping line, and the ball stays on it. Motion in a straight line does not have to be horizontal — only along a line that does not bend.

Can it be drawn on a horizontal line? Yes. What Fig. 4.3 does is mark positions along the direction of motion, with the starting point as origin. Since the motion is along one straight line, the positions of the ball can be laid out on a line in the same way; the fact that the real track slopes changes none of the distances along it. The tilt matters to how fast the ball rolls, not to how its positions are described.

Are distance and displacement equal? The ball rolls in one direction only, from O towards D, never turning back. With no reversal, the path length from O is exactly the straight-line distance from O. Reading Fig. 4.6, the segments are $OA = 40$ cm, $AB = 10$ cm, $BC = 20$ cm and $CD = 30$ cm, so measured from O:

Pause and Ponder, page 53. The box that follows Section 4.2, on average speed and average velocity.

Question 4

During a family road trip, you drive 200 km north in three hours. Afterwards, you drive 200 km south in two hours. Find the average speed and average velocity for your entire trip.

Solution. “Entire trip” means both legs together, so add the distances and add the times before dividing — not average the two separate speeds, which would give a different and wrong number.

The total distance travelled is the whole path:

$$\text{total distance} = 200 + 200 = 400\ \text{km}, \qquad \text{total time} = 3 + 2 = 5\ \text{h}$$

$$\text{average speed} = \frac{400\ \text{km}}{5\ \text{h}} = 80\ \text{km h}^{-1}$$

The displacement is the net change in position. Driving 200 km north and then 200 km south brings you back to where you started, so the two cancel exactly:

$$\text{displacement} = 200\ \text{north} + 200\ \text{south} = 0$$

$$\text{average velocity} = \frac{0}{5\ \text{h}} = 0\ \text{km h}^{-1}$$

Question 5

Under what condition(s) is the

(i) magnitude of average velocity of an object equal to its average speed?

(ii) magnitude of average velocity of an object zero while its average speed is not zero?

Solution. Both parts are settled by comparing the two numerators, since the time interval underneath is the same for both quantities. So the question is really: when does the magnitude of the displacement equal the distance travelled, and when is it zero while the distance is not?

(i) They are equal exactly when the object travels in a straight line in one direction, without turning back. Then every metre of path adds a metre to the displacement as well. The moment the object reverses, the path keeps growing while the displacement stops growing, and the average speed becomes the larger of the two. This is the note printed beside Section 4.2 in the chapter.

(ii) The displacement is zero when the object returns to its starting point, so the net change in position is nil — while the path it covered getting there and back is not, so the average speed is not zero. Sarang’s swim in Example 4.2 is exactly this: 50 m of path, zero displacement, average speed $1\ \text{m s}^{-1}$ and average velocity $0\ \text{m s}^{-1}$.

Common mistakes

• Averaging the two speeds in Question 4. The legs are $200/3 = 66.7$ km/h and $200/2 = 100$ km/h, and their mean, 83.3 km/h, is not the average speed. Average speed is total distance over total time, and the slower leg lasted longer, which is why the true answer, 80 km/h, is below the mean.
• Giving the average velocity in Question 4 as 80 km/h. The two legs are in opposite directions, so they cancel: displacement zero, average velocity zero. A journey can have a large average speed and no average velocity at all.
• Calling the rolling ball’s motion “not straight-line” because the track slopes. Straight-line motion means the path does not bend. A sloping straight track qualifies; a curved horizontal track would not.
• Assuming distance and displacement must differ. They differ only when the object turns back. In Question 3 the ball never reverses, so they are equal at every position — which is the point the question is making.
• Saying fuel depends on displacement because the car “ends up” somewhere. The engine burns fuel for the path, not the net position. The round trip with zero displacement is the case that settles it.

Practise next

• The end-of-chapter questions, Revise, Reflect, Refine, where Questions 1 to 3 put numbers on this same distinction and Question 16 works through a whole journey in four parts.
• Chapter 6, How Forces Affect Motion — its in-text questions take the velocity defined here and ask what changes it.