Fifteen centuries before the term "average speed" appeared in a physics textbook, Indian mathematicians were solving problems of rate, time, and distance with remarkable rigour. NCERT Chapter 4 (Exploration edition) acknowledges this heritage — this page goes deeper with full context, dates, authors, and solved examples. Aligned with CBSE syllabus 2026-27.
NCERT Science Class 9 Chapter 4 (Exploration edition) includes a dedicated box titled "India's Scientific Contributions". In that box, the textbook mentions two classical Indian texts — the Aryabhatiya and the Ganitakaumudi — as early examples of the mathematical treatment of speed and relative motion. This page expands on that box with full context, dates, authors, and the solved example from Ganitakaumudi that appears as NCERT Example 4.1.
The inclusion of this box reflects the NCERT's intent to situate modern science within a broader cultural and historical heritage. Understanding where these ideas came from makes the subject richer — and helps students see science not as a product of a single country or century, but as a cumulative human endeavour.
Q. What is the Aryabhatiya?
The Aryabhatiya is a concise Sanskrit treatise in 118 verses (shlokas), divided into four chapters covering mathematics and mathematical astronomy. It is one of the oldest surviving scientific texts from India and was widely influential across the medieval world — Arabic translations of the Aryabhatiya carried its ideas to the Islamic world, from where they eventually reached Europe.
Q. What does the Aryabhatiya say about speed?
The text establishes the relationship between speed, distance, and time in the context of calculating the positions of celestial bodies. Planetary positions were computed using the principle that if a planet covers a known distance in a known time, its speed can be determined — and its future position predicted. This is precisely:
$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$The distance unit used was the yojana and the time unit was typically a day (dina) or a specific astronomical period. The method is identical in structure to the average speed formula in today's NCERT textbook.
Q. What are Aryabhata's other celebrated contributions?
The Aryabhatiya contains several results that were far ahead of their time:
| Contribution | What Aryabhata said | Significance |
|---|---|---|
| Value of π (pi) | Approximated π ≈ 3.1416 (accurate to 4 decimal places) | One of the most accurate values known in the ancient world |
| Rotation of the Earth | Proposed that the Earth rotates on its axis — the apparent motion of stars is due to Earth's spin | A heliocentric-leaning insight, over a millennium before Copernicus |
| Length of the year | 365 days, 6 hours, 12 minutes, 30 seconds | Within a few minutes of the modern value (365 d 6 h 9 min 10 s) |
| Trigonometry (Jya) | Created the first table of sine values (called jya) | The word "sine" itself derives, through Arabic translation, from the Sanskrit jya |
Q. What is the Ganitakaumudi?
The Ganitakaumudi is a comprehensive Sanskrit mathematics text written by Narayana Pandita in the 14th century. It covers a wide range of topics: arithmetic operations, fractions, interest calculations, permutations and combinations (centuries before European treatments), magic squares, and problems of motion. The text is written in verse form (shloka), as was customary for Indian mathematical texts, and includes detailed worked examples (called udaharana).
Q. Why is the Ganitakaumudi relevant to Chapter 4 of Class 9 Science?
One of the problems in the Ganitakaumudi — which NCERT has adapted as Example 4.1 in Chapter 4 — involves two postmen walking toward each other at different speeds and asks how long it takes them to meet. This is a problem of relative speed and time, requiring exactly the same mathematical tools as modern average-speed problems.
Setup: The two postmen move toward each other, so their speeds add up. The combined rate at which the distance between them decreases is their relative speed.
Step 1 — Find the relative speed (combined closing rate):
$$\text{Relative speed} = \text{speed of P} + \text{speed of Q} = 9 + 5 = 14\,\text{yojanas per day}$$Step 2 — Find the time to meet:
$$t = \frac{\text{Total distance}}{\text{Relative speed}} = \frac{210}{14} = \mathbf{15\,\text{days}}$$Step 3 — Verify by finding how far each postman walks in 15 days:
| Postman | Speed (yojanas/day) | Distance in 15 days (yojanas) |
|---|---|---|
| P | 9 | 9 × 15 = 135 |
| Q | 5 | 5 × 15 = 75 |
Total distance covered: 135 + 75 = 210 yojanas ✓ — exactly the initial separation. The answer is confirmed.
Q. This problem uses speed = distance ÷ time. Is that the same formula as in today's NCERT?
Exactly the same. In modern notation, NCERT Eq. 4.1 defines average speed as total distance divided by total time taken. The Ganitakaumudi was applying the same relationship — to time and distance measured in the units of 14th-century India — roughly 660 years before this textbook was written.
A yojana (योजन) is an ancient Indian unit of distance. Its exact modern equivalent varies by source and historical period:
| Source / Period | Approximate equivalent |
|---|---|
| Arthashastra (Kautilya, ~300 BCE) | ~8 km |
| Astronomical texts (Aryabhatiya era) | ~13–15 km |
| Medieval texts (Ganitakaumudi era) | ~8–12 km |
| Buddhist texts (Pali literature) | ~7 km |
If we use the commonly cited value of approximately 12 km per yojana, the 210 yojanas in the Postman Problem represents roughly 2,500 km — comparable to the distance between Delhi and Kanyakumari. At 9 yojanas (≈ 108 km) per day, Postman P was covering a remarkable distance — perhaps the problem was purely mathematical rather than physically realistic. This is characteristic of classical Indian mathematical problems, which often used large or idealized numbers to test the method rather than to model a specific real journey.
Q. Why does NCERT include this history in a science chapter?
Including the history of scientific ideas does two things. First, it shows that the concepts being learned are not arbitrary — they grew out of real human problems and real intellectual effort over many centuries. Second, it places India's contribution squarely in the story of science, countering the mistaken notion that modern physics and mathematics are exclusively products of 17th–20th century Europe.
The concept of speed as the ratio of distance to time was not "invented" by Galileo or Newton. It was used by Aryabhata to calculate planetary positions in the 5th century CE, formulated into elegant word problems by Narayana Pandita in the 14th century, and is still the foundational definition in a Class 9 textbook today. The formula has persisted across 1,500 years and across civilisations — a sign of its fundamental correctness.
Q. Were there other ancient Indian contributions related to motion?
Yes. The Aryabhatiya also calculated the speeds of the five visible planets (Mercury, Venus, Mars, Jupiter, Saturn) in terms of the number of revolutions each completes in a mahayuga (a vast astronomical time cycle). By dividing the distance of one full revolution by the time period, Aryabhata effectively computed the average orbital speed of each planet. This was applied astronomy grounded in the same mathematical framework as today's speed = distance ÷ time.
The Surya Siddhanta (c. 400 CE, author unknown) similarly computes the linear speed of planets in yojanas per civil day. The Brahmasphutasiddhanta by Brahmagupta (628 CE) extended these ideas and introduced corrections for orbital perturbations — a precursor to what would later be called orbital mechanics.
Section 4.1.3 of the current NCERT Class 9 Science textbook defines average speed using the formula:
$$\text{Average speed} = \frac{\text{Total distance travelled}}{\text{Total time taken}} \qquad (\text{Eq. 4.1})$$This is structurally and mathematically identical to what the Aryabhatiya uses for planetary speeds and what the Ganitakaumudi uses for the Postman Problem. The symbols have changed (Sanskrit shlokas → modern algebraic notation), the units have changed (yojanas and days → metres and seconds), and the precision has improved — but the underlying idea is unchanged.
When you solve an average speed problem in your exam, you are using a method that was used to predict the position of Jupiter in the 5th century CE. That is a remarkable continuity of human thought.
For the full treatment of average speed with the modern formula, solved examples, and unit conversion, see Average Speed and Velocity (C02).