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Measurement of Time and Motion

NCERT Class 7 · Science Based on NCERT Class 7 Science textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter explores how humans have measured time from ancient to modern times, introduces the simple pendulum as a reliable timekeeping device, and defines speed and types of motion. The one big idea is that all clocks rely on periodic repeating processes, and speed is the distance covered per unit time, which helps us compare how fast or slow objects move. Students must understand the relationship between distance, time, and speed, and distinguish between uniform and non-uniform linear motion.
Key Concepts (13)
Time period
The time taken by a pendulum to complete one oscillation is called its time period.
e.g. If a pendulum takes 2 seconds to swing from one extreme to the other and back, its time period is 2 seconds.
Oscillation
One complete to-and-fro motion of the pendulum from its mean position to one extreme, to the other extreme, and back to the mean position.
e.g. When a pendulum bob starts at O, goes to A, then to B, and returns to O, it has completed one oscillation.
Simple pendulum
A simple pendulum consists of a small metallic ball (called the bob) suspended from a rigid support by a long thread.
e.g. A stone tied to a string and hung from a hook is a simple pendulum.
Speed
The distance covered by an object in a unit time is called its speed.
e.g. If a bicycle covers 4 metres in 1 second, its speed is 4 m/s.
Average speed
The total distance covered divided by the total time taken is called the average speed.
e.g. If a car travels 150 km in 3 hours, its average speed is 50 km/h, even if it sometimes went faster or slower.
Uniform linear motion
An object moving along a straight line with a constant speed is said to be in uniform linear motion.
e.g. A train moving at a constant 60 km/h on a straight track between two stations is in uniform linear motion.
Non-uniform linear motion
If the speed of an object moving along a straight line keeps changing, it is said to be in non-uniform linear motion.
e.g. A car moving in city traffic that speeds up and slows down is in non-uniform linear motion.
SI unit of time
The SI unit of time is the second, symbol s.
e.g. 60 seconds make 1 minute, and 60 minutes make 1 hour.
SI unit of speed
The SI unit of speed is metre per second, expressed as m/s.
e.g. A runner moving at 8 m/s covers 8 metres every second.
Speedometer
An instrument in vehicles that measures and displays the vehicle's speed in km/h.
e.g. The dial on a scooter dashboard showing 40 km/h is the speedometer.
Odometer
An instrument in vehicles that measures the distance travelled by the vehicle in kilometres.
e.g. The reading on a car's dashboard that shows 12,500 km is the odometer.
Ghatika (or ghati)
A traditional Indian unit of time equal to 24 minutes, measured by the sinking bowl water clock (Ghatika-yantra).
e.g. A 24-hour day was divided into 60 ghatis.
Mean position
The position of the pendulum bob when it is at rest, hanging vertically downward.
e.g. When a pendulum is not swinging, the bob is at its mean position.
How It Works
Measuring time using a simple pendulum
  1. Tie a bob at one end of a string and fix the other end to a rigid support.
  2. Gently move the bob slightly to one side and release it without pushing.
  3. Let the pendulum oscillate and use a stopwatch to measure the time for 10 complete oscillations.
  4. Divide the total time by 10 to get the time period of the pendulum.
  5. Repeat 3-4 times to confirm the time period is constant for a given length.
💡 The time period depends only on the length of the pendulum, not on the mass of the bob. Do not push the bob while releasing it.
Constructing a simple water clock
  1. Cut a transparent plastic bottle into two halves roughly in the middle.
  2. Make a small hole in the bottle cap using a drawing pin.
  3. Place the upper part of the bottle inverted over the lower half.
  4. Fill the upper part with water (add ink for visibility).
  5. Using a watch, mark the water level in the lower part every one minute until all water drips down.
  6. To use, pour water back into the top part; each mark indicates one minute has passed.
💡 The water clock is not very accurate because the flow rate decreases as the water level drops.
Calculating speed
  1. Identify the total distance covered by the object.
  2. Identify the total time taken to cover that distance.
  3. Use the formula: Speed = Total distance covered / Total time taken.
  4. Ensure units are consistent (e.g., metres and seconds for m/s, or kilometres and hours for km/h).
💡 Speed calculated this way is average speed; the object may not have moved at the same speed throughout.
Calculating distance or time using speed
  1. If speed and time are known, use: Total distance covered = Speed × Total time taken.
  2. If distance and speed are known, use: Total time taken = Total distance covered / Speed.
💡 Always check that units match — if speed is in km/h, time must be in hours to get distance in km.
Exam Traps — Don't Make These Mistakes
⚠ Confusing oscillation with one swing
✗ One oscillation is when the bob moves from one extreme to the other.
→ One oscillation is a complete to-and-fro motion — from mean to one extreme, to the other extreme, and back to mean (or from one extreme to the other and back to the same extreme). A single swing is only half an oscillation.
✓ One oscillation is the complete to-and-fro motion of the bob, starting from the mean position, going to one extreme, then to the other extreme, and returning to the mean position.
⚠ Writing 'sec' or 'hrs' for units
✗ The time taken is 10 sec. The speed is 60 km/hr.
→ The correct symbols are 's' for second and 'h' for hour. 'sec' and 'hrs' are incorrect. Also, a full stop is not written after the symbol except at the end of a sentence.
✓ The time taken is 10 s. The speed is 60 km/h.
⚠ Forgetting to convert units in speed problems
✗ Speed = 3.6 km / 15 min = 0.24 km/min, and leave it as the answer.
→ The question often asks for speed in m/s. Students must convert km to m (multiply by 1000) and minutes to seconds (multiply by 60) before dividing.
✓ Speed = (3.6 × 1000 m) / (15 × 60 s) = 3600 m / 900 s = 4 m/s.
⚠ Thinking the time period depends on the bob's mass
✗ A heavier bob will have a longer time period.
→ The time period of a simple pendulum depends only on its length, not on the mass of the bob. All pendulums of the same length have the same time period at a given location.
✓ The time period of a simple pendulum depends on its length but not on the bob's mass.
⚠ Confusing uniform and non-uniform motion
✗ A car moving on a straight road is always in uniform motion.
→ Uniform motion requires constant speed. A car on a straight road may speed up, slow down, or stop, so its motion is often non-uniform unless it maintains exactly the same speed.
✓ Uniform linear motion means moving along a straight line with constant speed, covering equal distances in equal intervals of time. If speed changes, it is non-uniform motion.
Compare & Contrast
Speed over time
Uniform linear motion
Non-uniform linear motion
In uniform linear motion, the object covers equal distances in equal intervals of time (constant speed). In non-uniform linear motion, it covers unequal distances in equal intervals of time (changing speed).
Principle of time measurement
Sundial
Water clock
A sundial measures time based on the changing position of a shadow cast by the Sun, so it works only during daytime. A water clock measures time based on the flow of water into or out of a vessel and can be used at any time.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 Very Short Answer (1 mark), 1 Short Answer (3 marks) on pendulum or speed, 1 Long Answer (5 marks) involving numerical on speed/distance/time or distinguishing motion types.
Most asked: Definition and calculation of speed (including unit conversions) · Time period of a simple pendulum and factors affecting it · Distinguishing between uniform and non-uniform motion with examples · Numerical problems on speed, distance, and time
Don't skip: Numerical problems calculating speed, distance, or time with unit conversions (e.g., km/h to m/s); Explaining the time period of a pendulum and the effect of changing length; Differentiating uniform and non-uniform motion with a table or example
One-Line Revision (read aloud before the exam)
  1. The SI unit of time is the second (s).
  2. 60 seconds = 1 minute, 60 minutes = 1 hour.
  3. The time period of a simple pendulum is the time taken for one complete oscillation.
  4. The time period of a pendulum depends only on its length, not on the mass of the bob.
  5. A simple pendulum consists of a bob suspended from a rigid support by a long thread.
  6. Speed is the distance covered by an object in a unit time.
  7. Speed = Total distance covered / Total time taken.
  8. The SI unit of speed is metre per second (m/s).
  9. Average speed is used when an object does not move at a constant speed.
  10. Uniform linear motion means moving along a straight line with constant speed.
  11. Non-uniform linear motion means moving along a straight line with changing speed.
  12. A sundial measures time using the Sun's shadow.
  13. A water clock measures time using the flow of water.
  14. A speedometer shows the speed of a vehicle in km/h.
  15. An odometer measures the total distance travelled by a vehicle.
  16. One oscillation of a pendulum is one complete to-and-fro motion.

MCQs — 10 Questions with Answers

Q1. Which of the following was NOT used in ancient times to measure time?

  • A. Sundial
  • B. Water clock
  • C. Atomic clock ✓
  • D. Candle clock

Answer: C — Atomic clocks are modern inventions; sundials, water clocks, and candle clocks were all used in ancient times.

Q2. What does a hourglass use to measure time?

  • A. Flow of water
  • B. Flow of sand from one bulb to another ✓
  • C. Burning of wax or tallow
  • D. Position of the sun's shadow

Answer: B — An hourglass measures time by the flow of sand from the upper bulb to the lower bulb.

Q3. The time taken by a pendulum to complete one oscillation is called its:

  • A. Amplitude
  • B. Frequency
  • C. Time period ✓
  • D. Wavelength

Answer: C — The time period is defined as the time taken to complete one full oscillation.

Q4. Which ancient Indian mathematical text first mentioned the sinking bowl water clock?

  • A. Arthasastra
  • B. Works of Aryabhata ✓
  • C. Works of Varahamihira
  • D. Sardulakarnavadana

Answer: B — Aryabhata first mentioned the Ghatika-yantra (sinking bowl water clock) in his astronomical texts.

Q5. A student creates a water clock at home. If she wants the water to drip faster, which change should she make?

  • A. Make the hole bigger in the cap ✓
  • B. Add more color to the water
  • C. Use a taller bottle
  • D. Use colder water

Answer: A — A bigger hole allows water to flow out faster, so the water level drops more quickly.

Q6. If a pendulum of length 100 cm has a time period of 2 seconds, what will happen to the time period if the length is increased to 200 cm, keeping everything else the same?

  • A. It will decrease to 1 second
  • B. It will increase to 3 seconds ✓
  • C. It will remain 2 seconds
  • D. It will increase but by less than 1 second

Answer: B — Time period increases as length increases, and doubling the length approximately increases the time period from 2 to about 2.8 seconds (approximately 3 seconds).

Q7. Why can atomic clocks measure time much more accurately than pendulum clocks?

  • A. They use electricity instead of gravity
  • B. They use rapid vibrations of atoms which are extremely constant and unaffected by environmental changes ✓
  • C. They have more gears and springs
  • D. They are made of stronger materials

Answer: B — Atomic vibrations are extremely constant and stable, allowing atomic clocks to lose only 1 second in millions of years.

Q8. Prerna noticed that at the Olympics, even when two sprinters seemed to finish together, the measurement identified a winner. Which modern technology makes this possible?

  • A. Simple stopwatch with manual timing
  • B. Pendulum clocks like those in schools
  • C. Advanced electronic timers and sensors that measure time to fractions of a second ✓
  • D. Sundials and water clocks placed at the finish line

Answer: C — Olympic timing uses advanced electronic systems that can measure time differences of fractions of a second to determine the exact winner.

Q9. A student conducted Activity 8.2 with two pendulums of the same length but different bob masses. What would she observe?

  • A. The pendulum with heavier bob completes more oscillations in 1 minute
  • B. Both pendulums have the same time period because time period depends only on length ✓
  • C. The pendulum with lighter bob has a shorter time period
  • D. The time period increases proportionally with the mass of the bob

Answer: B — Time period of a pendulum depends only on its length, not on the mass of the bob, so both would have identical time periods.

Q10. The Samrat Yantra at Jantar Mantar, Jaipur is a 27-metre-tall structure whose shadow moves at 1 millimetre per second. How is this property useful for measuring time?

  • A. The slow shadow movement allows very precise time measurements in small intervals ✓
  • B. The height makes it visible from far away
  • C. It can measure time only during daylight hours like regular sundials
  • D. It measures Indian Standard Time automatically without any correction

Answer: A — The precise rate of shadow movement (1 mm per second) allows the Samrat Yantra to measure very small time intervals as short as 2 seconds.

Flashcards

What is a simple pendulum?

A small metallic ball (bob) suspended by a long thread from a rigid support that oscillates back and forth.

Define time period of a pendulum.

The time taken by a pendulum to complete one complete oscillation from mean position to one extreme, then other extreme, and back to mean.

What does a sundial use to measure time?

The changing position of the shadow cast by the Sun on a marked scale throughout the day.

How does a water clock measure time?

By measuring the flow of water from one vessel to another, using the rate of water flow to mark time intervals.

What factor does NOT affect the time period of a pendulum?

The mass of the bob; time period depends only on the length of the pendulum.

What is an oscillation of a pendulum?

One complete back-and-forth motion of the pendulum bob from one extreme position through mean position to the other extreme and back.

What is the SI unit of time?

The second, with symbol s, where 60 seconds equal 1 minute and 60 minutes equal 1 hour.

How do modern atomic clocks measure time?

By using rapid vibrations from specific atoms that oscillate at a constant rate to mark equal intervals of time.

What is the mean position of a pendulum?

The resting position of the pendulum bob when it hangs vertically downward without any motion.

Why was the pendulum clock a major breakthrough?

It provided much more accurate timekeeping than earlier mechanical clocks by using the constant time period of a pendulum.

Important Board Questions

What is meant by one oscillation of a pendulum? [1 mark]

From mean position through one extreme to other extreme and back to mean; or from one extreme to other extreme and back to same extreme.

How do modern atomic clocks differ from pendulum clocks in terms of accuracy? [2 marks]

Pendulum clocks lose 10 seconds per day; atomic clocks use vibrations of atoms and lose only 1 second in millions of years. Mention the reason: atoms vibrate at constant rate unaffected by environment.

Explain with steps how you would measure the time period of a simple pendulum using Activity 8.2. Why do we measure time for 10 oscillations instead of just 1? [3 marks]

Steps: fix pendulum, release bob, start stopwatch, count 10 oscillations, record time, divide by 10 to get time period. Reason: measuring 10 oscillations reduces error because timing error spread over 10 gives more accurate average; one oscillation timing is too quick and prone to human reaction error.

Describe the construction and working of a simple water clock as shown in Activity 8.1. How would you use it to measure time after construction? [5 marks]

Construction: cut plastic bottle in half, make hole in cap, invert upper half over lower half, fill with water. Label with marks every 1 minute. Working: water drips at constant rate due to gravity, each mark indicates 1 minute passed. Draw and label: water level in upper part, hole, marks on lower part at 1-min, 2-min, 3-min intervals, arrow showing water flow direction.

Assertion-Reason Questions for Measurement of Time and Motion

Q1. Assertion (A):

A simple pendulum exhibits periodic motion, meaning it repeats the same path in the same time interval.

Reason (R):

The pendulum bob oscillates between two extreme positions through a mean position, and gravity continuously pulls it back.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true. The assertion correctly defines periodic motion based on the textbook description. The reason explains WHY the motion is periodic—gravity restores the bob to mean position, causing repetition. The reason correctly explains the assertion.

Q2. Assertion (A):

The Ghatika-yantra water clock became inaccurate when the outflow-type water clock was in use, leading to its development.

Reason (R):

As water level decreased in the outflow-type clock, the pressure reduced, causing the flow rate to decrease and making timing inconsistent.

Answer: B — Both A and R are true, but R is NOT the correct explanation of A — Both statements are true. The text confirms Ghatika-yantra was developed due to inaccuracy of earlier water clocks, and explains the reason as decreasing flow rate with lower water levels. However, the reason (water level causing pressure changes) doesn't directly explain why Ghatika-yantra was specifically developed—rather, it explains the problem that Ghatika-yantra solved. The reason is correct but not the explanation of the assertion.

Q3. Assertion (A):

Christiaan Huygens invented the pendulum clock based on observations made by Galileo Galilei.

Reason (R):

Galileo discovered that a swinging lamp always takes the same time for each swing, regardless of the swing amplitude.

Answer: C — A is true but R is false — The assertion is true according to the text. However, the reason is incomplete or misleading. The text states Galileo observed consistent time but doesn't mention that the time was independent of amplitude (swing angle). The statement about amplitude constancy is not explicitly in the provided material, though it's physically true. The reason lacks the textbook's specific wording and may be considered unsupported by the source material.

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Case-Based Questions (CBQ) for Measurement of Time and Motion

Case Study:

A museum in Rajasthan is designing an educational exhibit about timekeeping. They have a 3-metre sundial model and a working water clock model. Visitors are asked to observe how the sundial's shadow moves throughout the day and to measure time using the water clock by observing marked levels. The water clock model has 10 marks, each representing 1 minute. A group of students visits on a cloudy morning, and the museum staff explain that while both devices measure time, one works only in sunlight while the other works in any weather condition.

Q1. Why would the sundial model be less useful on the cloudy morning compared to a typical sunny day?

  • A. The 3-metre size is too small to cast clear shadows
  • B. Clouds block sunlight, preventing clear shadow formation for time measurement ✓
  • C. The model's markings fade in humidity from clouds
  • D. Sundials automatically reset on cloudy days and cannot show time

Answer: B

Q2. Based on the water clock model with 10 marks representing 10 minutes, what principle allows this device to work in any weather?

  • A. Water clocks use gravity to maintain constant flow, independent of light ✓
  • B. Water clocks have electronic sensors that measure time
  • C. Water clocks use only the temperature of water to measure time
  • D. Water clocks reflect light internally to measure time without sunlight

Answer: A

Q3. If a student uses the water clock model with 10 marks to measure 5 minutes, approximately how many millilitres of water should have dripped if the total capacity is 500 ml?

  • A. 250 ml, because half the marks represent half the capacity ✓
  • B. 50 ml, because half of 10 marks (5 marks) would be half the water per mark
  • C. 500 ml, because the entire clock must be used
  • D. Cannot determine without knowing the flow rate per mark

Answer: A

Q4. Why is the water clock model more reliable for continuous timekeeping at a museum than a full-size Samrat Yantra-style sundial?

  • A. Water clocks are smaller and cheaper to build
  • B. Water clocks function consistently regardless of weather and can measure any time of day ✓
  • C. Sundials can only work in India and not in museums in other countries
  • D. Water clocks were invented more recently and use modern technology

Answer: B

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