NCERT Solutions for Class 9th Science Chapter 4 Bridging Science and Society — Kinematic equations
Book page 65 Updated on2026-09-19
Q1.
Can you now understand why it is important to maintain a safe distance from the vehicle moving ahead of your vehicle (Fig. 4.20) and how this distance needs to be adjusted given your initial velocity?
Fig. 4.20, page 65 — safe distance between two moving vehicles (redrawn as a labelled sketch from the illustration in the textbook).
Answer
Yes. A vehicle cannot stop where the driver decides to stop — it stops where physics allows, and that place is set by u², not by u.
stopping distance = reaction distance + braking distance
= u tr + u² / (2|a|) [the second term from v² = u² + 2as with v = 0]
Using the chapter's own braking figure of |a| = 4 m s⁻² and a reaction time tr = 1 s:
Initial velocity u
Reaction distance u tr
Braking distance u²/2|a|
Total stopping distance
36 km h⁻¹ = 10 m s⁻¹
10 m
12.5 m
22.5 m
54 km h⁻¹ = 15 m s⁻¹
15 m
28.1 m
43.1 m
108 km h⁻¹ = 30 m s⁻¹
30 m
112.5 m
142.5 m
Going from 54 to 108 km h⁻¹ doubles the speed but makes the stopping distance more than three times longer — because the braking part alone becomes four times longer.
Why it happens: during braking the vehicle loses kinetic energy at a roughly steady rate set by the friction the tyres can supply, and the speed enters that balance as a square. The reaction part is different in nature: it is a stretch of road covered at full speed with no braking at all, so it simply grows in proportion to u. This is why a fixed "keep 20 m behind" rule is useless — the safe gap must grow with speed, which is why drivers are taught a time gap (2–3 s) instead.
Did you know? Anything that lowers |a| — a wet or gravelly road, worn tyres, a heavily loaded truck — stretches the braking term inversely. Halve the grip and every braking distance in the table doubles. Vehicle-to-vehicle (V2V) technology, now being developed in India and elsewhere, attacks the other term instead: it lets the vehicle ahead warn you electronically, cutting the reaction time far below a human's.