Plotting a graph is a skill — not just colouring dots on paper. This activity teaches the full process: scale selection, axis labelling, point plotting, and reading what the resulting shape tells you about the motion. From NCERT Chapter 4 (Exploration edition) Class 9 Science. Aligned with CBSE syllabus 2026-27.
Aim: To plot position-time graphs for (a) a vehicle in uniform motion and (b) a vehicle in uniformly accelerated motion, and to identify the motion type from the shape of each graph.
Materials needed: Graph paper (1 mm or 2 mm squares), sharp pencil, ruler (30 cm), eraser, and the data tables from NCERT Chapter 4.
This activity directly builds the skill needed to understand position-time graphs (C04) — the single most important graph type in the chapter. Once you can plot from data, reading and interpreting graphs from questions becomes straightforward.
2. Data — NCERT Table 4.3 (Uniform Motion)
NCERT Table 4.3 gives the position of a vehicle moving at constant speed along a straight road:
Time t (s)
Position s (m)
Distance in 2 s interval (m)
0
0
—
2
40
40
4
80
40
6
120
40
8
160
40
Equal distances (40 m) in equal time intervals (2 s) → this is uniform motion. The speed is $40/2 = 20\,\text{m s}^{-1}$. You should expect a straight line through the origin when you plot this data.
3. Step-by-Step Procedure (7 Steps)
Step 1 — Draw the axes
Draw two perpendicular lines on your graph paper. The horizontal axis (x-axis) is for time (t) and the vertical axis (y-axis) is for position (s). Mark the origin O where they meet. Both axes must start from zero.
Step 2 — Choose and mark scales
Decide how many units of the physical quantity each small square (or each large square) on the graph paper represents. For Table 4.3: time goes from 0 to 8 s, position from 0 to 160 m. A suitable scale might be 1 cm = 1 s on the x-axis and 1 cm = 20 m on the y-axis. Write the scale on the graph ("Scale: x-axis: 1 cm = 1 s; y-axis: 1 cm = 20 m").
Step 3 — Label axes with quantity and unit
Write "Time (s)" along the x-axis and "Position (m)" along the y-axis. Mark the values at regular intervals: 0, 2, 4, 6, 8 on x-axis and 0, 40, 80, 120, 160 on y-axis.
Step 4 — Plot the data points
For each row in Table 4.3, locate the corresponding t value on the x-axis and the s value on the y-axis. Mark the point where these two values meet with a small, neat dot (or ×). Do this for all five rows: (0,0), (2,40), (4,80), (6,120), (8,160).
Step 5 — Draw the best-fit line
Place your ruler so that it passes through (or very near) all plotted points. Draw a single straight line. Do not connect dot-to-dot like a join-the-dots puzzle — draw one smooth line that best represents the data. In this case the five points will all lie exactly on a straight line because the motion is perfectly uniform.
Step 6 — Give the graph a title
Write "Position-Time Graph for a Vehicle in Uniform Motion" (or a similar title) at the top of the graph. A graph without a title is incomplete.
Step 7 — Read and interpret
Look at the shape. A straight line through the origin confirms uniform motion with constant speed. The slope of the line equals the speed. To find slope: pick two points on the line (not necessarily data points) and calculate (change in s) ÷ (change in t). For this graph you should get 20 m s⁻¹.
4. Scale Selection Guidance
Q. How do I choose a scale so the graph is neither too cramped nor too spread out?
A well-chosen scale makes the graph fill at least half the paper in each direction. Use this method:
Find the maximum value of each quantity. Divide it by the number of large squares available on that axis (typically 10–15 on standard graph paper). Round up to a convenient number like 5, 10, 20, 25, or 50. That becomes your scale unit.
For Table 4.3: maximum t = 8 s, maximum s = 160 m. If the paper has 10 large squares on each axis: time scale = 8/10 = 0.8 → round up to 1 s per cm. Position scale = 160/10 = 16 → round up to 20 m per cm. This gives a graph 8 cm wide and 8 cm tall — well proportioned.
⚠️ Common mistakes in scale selection: (a) Using different scales on the same axis for different parts of the range — always keep the scale uniform. (b) Starting the axis at a value other than zero without marking a clear origin break. (c) Choosing a scale that leaves all data points cramped into one corner.
5. Table 4.4 — Accelerated Motion (Parabola)
NCERT Table 4.4 gives the position of a vehicle that starts from rest and accelerates uniformly:
Time t (s)
Position s (m)
0
0
2
1
4
4
6
9
8
16
10
25
12
36
Pattern: The positions are 0, 1, 4, 9, 16, 25, 36 — perfect squares! This reveals that $s \propto t^2$. Since $s = \frac{1}{2}at^2$ for motion from rest, the acceleration is:
When you plot this data, the result is a smooth upward-curving parabola, not a straight line. The curve confirms that the motion is non-uniform (accelerated). The slope of the curve (tangent at any point) gives the instantaneous velocity at that moment — a technique covered in Activity 4.4 (C19).
Summary — What the graph shape tells you:
Straight line through origin → uniform motion, constant speed, zero acceleration.
Upward-curving parabola → uniformly accelerated motion from rest, $s \propto t^2$.
6. Graph Reading Practice
Q1. From the Table 4.3 graph (straight line), what is the position of the vehicle at t = 3 s? What is the speed?
Show Answer
The graph is a straight line. At $t = 3\,\text{s}$, read up to the line and across: $s = 60\,\text{m}$. (Alternatively: speed = 20 m s⁻¹, so in 3 s the vehicle covers 60 m.)
Wait — check: the table gives s = 1 at t = 2 and s = 4 at t = 4. The pattern is $s = (t/2)^2 = t^2/4$. At t = 5: $s = 25/4 = \mathbf{6.25\,\text{m}}$. This is between the t = 4 value (4 m) and t = 6 value (9 m) — consistent with a smooth curve. A value of 6.25 m at t = 5 is correct and can be confirmed by reading the parabola on the graph.
Q3. Two vehicles A and B have p-t graphs that are both straight lines through the origin. A's line is steeper. What does this tell you?
Show Answer
Both are in uniform motion (straight lines). The slope of a p-t graph = velocity. A steeper slope means a larger slope value, hence a higher velocity. Vehicle A is moving faster than vehicle B. This is the comparison shown in NCERT Example 4.7.
📚 More from Chapter 4 — Describing Motion Around Us
