NCERT Solutions for Class 9th Science Chapter 4 Activity 4.1: Let us analyse — Distance travelled and displacement
Book page 51 Updated on2026-09-08
Q1.
As shown in Fig. 4.5, a ball is thrown vertically upwards from O. It moves up straight till B and then falls back to O. Can this be considered a motion in a straight line?
Answer
Yes. The whole journey — up from O to B and down again from B to O — happens along one and the same vertical straight line.
Why it happens: motion in a straight line does not mean the object must keep going one way. It only means the path is a straight line. Here the ball retraces the very same line on the way down; Fig. 4.5 draws the up-leg and the down-leg as two separate dotted lines only so that the marked positions A, B and C do not overlap on the page. In reality both legs lie on top of each other.
Check it yourself: because the ball does turn back at B, this is a case where distance travelled and magnitude of displacement will part company — exactly what Table 4.1 is designed to show.
Q2.
For this motion, fill up the values in Table 4.1.
Answer
Reading Fig. 4.5: O is at 0 cm, A at 40 cm, the highest point B at 140 cm, and C at 80 cm — but C is marked on the downward leg, so the ball reaches C only after it has already come down 60 cm from B.
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
at C: distance = OB + BC = 140 cm + (140 cm − 80 cm) = 140 cm + 60 cm = 200 cm
displacement = position of C − position of O = 80 cm − 0 cm = 80 cm upward
back at O: distance = OB + BO = 140 cm + 140 cm = 280 cm
displacement = 0 cm − 0 cm = 0 cm
Q3.
Analyse the data filled in Table 4.1 and choose which of the following is true for displacement: (i) It is never zero. (ii) Its magnitude can be greater than the total distance travelled. (iii) Its magnitude is less than or equal to the total distance travelled. (iv) Its magnitude is less than the total distance travelled in all cases.
Answer
The correct statement is (iii) Its magnitude is less than or equal to the total distance travelled.
Test each option against the table:
(i) is false — at the last row the ball is back at O and the displacement is exactly 0 cm.
(ii) is false — at C the displacement is 80 cm while the distance travelled is 200 cm. The displacement can never win, because it is only the straight-line gap between the two end positions.
(iii) is true — at A both are 40 cm (equal); everywhere after the ball turns back, the displacement is smaller.
(iv) is false — it says "in all cases", but at A they are equal, so "less than" does not hold in every case.
Why it happens: the shortest route between two points is the straight line joining them. The displacement is that straight-line gap; the distance travelled is the length of the route actually taken. A route can never be shorter than the straight line, so magnitude of displacement ≤ distance travelled, with equality only when the route is the straight line — that is, when the object never turns back.