NCERT Solutions for Class 9th Science Chapter 4 In-text Questions — Position-time graphs

Book page 59 Updated on2026-09-08

Q1.

What does the shape of the position-time graph indicate about the nature of motion?

Answer

The shape tells you at once whether the velocity is constant or changing, because the slope of a position–time graph is the velocity.

Shape of the position–time graph	What it means	Reason
Straight line, sloping	Constant velocity (uniform motion)	Equal displacements in equal times, so the slope never changes
Straight line parallel to the time axis	Object at rest	Position does not change with time, so the slope is zero
Curve getting steeper	Velocity increasing — accelerated motion	Larger displacements in successive equal time intervals
Curve getting flatter	Velocity decreasing	Smaller displacements in successive equal time intervals

The book's own two examples make it concrete. In Fig. 4.13a the object covers 20 m between 2 s and 3 s and again 20 m between 5 s and 6 s — equal displacements in equal times, so the graph is straight and the velocity is constant. In Fig. 4.13b the displacement between 4 s and 6 s is smaller than between 10 s and 12 s — the graph curves upward and the velocity is increasing.

Why it happens: velocity is defined as change in position ÷ change in time, and on this graph "change in position" is the rise and "change in time" is the run. So velocity is the steepness. A shape with fixed steepness must mean fixed velocity; a shape whose steepness changes must mean changing velocity, which is exactly acceleration.

Q2.

Which physical quantities can be obtained from a position-time graph?

Answer

Three things can be pulled straight off it:

The position of the object at any instant — read the Y-value directly above that time.
The displacement between any two instants — subtract the two Y-values, s₂ − s₁.
The average velocity between those instants — the slope of the line joining the two points.

v = BC / CA = (s₂ − s₁) / (t₂ − t₁) [Eq. 4.2a]
using Fig. 4.14: v = (80 m − 40 m) / (4 s − 2 s) = 40 m / 2 s = 20 m s⁻¹

You can also tell, without any calculation, whether the motion is uniform (straight line), accelerated (curve) or at rest (line parallel to the time axis) — and by comparing two lines on the same axes, which object is faster (Example 4.7: the steeper line has the larger velocity).

Why it happens: the graph stores position as a function of time, and every one of these quantities is built out of position and time alone. What it cannot give you directly is the acceleration — for that you would need how the slope itself is changing, which is a further step you will meet in higher grades.

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