Measurement Of Time And Motion
Important Notes - Class 7 Science (Curiosity) | Complete Learning Material
1. Introduction
Prerna and her sister were watching a sports channel. Prerna loved running and was the fastest girl in her district's 100-metre sprint. She was training for the state level and dreamed of running for India. While watching old Olympic races, Prerna was amazed at how accurately the time was measured, even when runners finished together. At school, they used a stopwatch to time races and compare the results.
Prerna's mother wore a watch, her sister checked the time on a phone, and her uncle had a Braille watch and a talking watch. There was also a large clock at school. Prerna wondered how people in the past told the time without these devices.
2. Measurement of Time
Long ago, humans became interested in keeping track of time. They noticed that many natural events happened in regular cycles, such as the rising and setting of the Sun, the phases of the Moon and the changing seasons. These cycles helped people create calendars. A day was defined by the cycle of the Sun rising and setting.
People also wanted to know the time during the day. Since there were no clocks or watches, they invented devices to measure smaller parts of the day and mark equal intervals. Some of the earliest devices used for measuring time within a day were:
Sundials: These use the shadow cast by the Sun on a fixed surface to show the time of day. As the Sun appears to move across the sky, the shadow changes position.
Water clocks: These measure time by the steady flow of water from one container to another or by the sinking of a bowl that fills with water.
Hourglasses: These measure time by the flow of sand from an upper bulb to a lower bulb through a narrow neck.
Candle clocks: These are candles with marks. As the candle burns down, the marks indicate the passage of time.
The world's largest stone sundial, called the Samrat Yantra, was built about 300 years ago at the Jantar Mantar in Jaipur, Rajasthan. Jantar Mantar is a UNESCO World Heritage site containing a group of astronomical instruments.
The Samrat Yantra stands 27 metres tall. Its shadow moves very slowly, about 1 millimetre every second, and falls on a scale that can measure time as precisely as every 2 seconds. Like all sundials, it shows local solar time, so a small correction is needed to convert this to Indian Standard Time.
Constructing a Simple Water Clock
A water clock measures time by the flow of water from one container to another. The water flow slows as the water level falls. Marking the water level at equal time intervals gives the clock its scale.
Materials required:
Used transparent plastic bottle of 1/2 litre or larger, with cap
Drawing pin
Water
Ink or food colour, if desired
1. Cut the plastic bottle into two halves, roughly in the middle.
2. Use a drawing pin to make a small hole in the cap of the bottle.
3. Place the upper part of the bottle, with the hole in the cap, upside down on the lower half so that water from the upper part can drip into the lower part.
4. Fill the upper part with water. You can add a few drops of ink or food colour to make the water level easier to see.
5. As water drips into the lower part, use a watch to mark the water level at regular intervals, for example, every minute, until all the water has dripped down. These marks form the scale of your water clock.
How to use the water clock:
Resetting: Pour the water from the lower part back into the upper part to start again.
Timing: Watch the water drip into the lower part and note when the water reaches each previously marked level. Each mark represents a fixed passage of time, for example, one minute.
The earliest mention of measuring time by shadows occurs in the Arthashastra by Kautilya, written between the 2nd century BCE and the 3rd century CE.
Around 530 CE, Varahamihira described a precise method of calculating time using the shadow of a vertical stick.
Water clocks in which water flowed out of a vessel were described in ancient texts such as the Arthashastra and the Sardulakarnavadana.
These early water clocks were not very accurate because the flow of water slowed as the water level dropped.
To improve accuracy, the sinking-bowl water clock, called the Ghatika-yantra, was developed and mentioned by astronomers including Aryabhata.
The Ghatika-yantra was used in Buddhist monasteries, royal palaces and town squares. When the bowl sank, the passage of time was announced by drums, conch shells or gongs.
Although pendulum clocks replaced the Ghatika-yantra by the late 19th century, it continued to be used in some religious places for rituals.
As human civilisation advanced and long-distance travel became common, precise timekeeping became more important. This led to the development of mechanical clocks driven by weights, gears and springs from the 14th century onwards. The invention of the pendulum clock in the 17th century was a major breakthrough that greatly improved the accuracy of mechanical clocks.
Know a scientist: Galileo Galilei
The pendulum clock was invented in 1656 and patented in 1657 by Christiaan Huygens (1629-1695). Huygens was inspired by earlier observations made by Galileo Galilei (1564-1642). Galileo noticed a lamp swinging in a church and, using his own pulse to measure time, found that the lamp took nearly the same amount of time for each swing. After testing different pendulums, Galileo discovered that the time for one complete swing remains nearly the same for a pendulum of fixed length. This observation led to the development of accurate pendulum clocks.
3. The Simple Pendulum
A simple pendulum consists of a small metal ball, called the bob, suspended from a rigid support by a long thread or light rod.
When the bob is at rest, it is in the mean position. If the bob is displaced slightly to one side and released, it swings back and forth in an oscillatory motion.
This motion is periodic because it repeats the same path after a fixed interval of time.
One complete oscillation occurs when the bob, starting from the mean position O, moves to the extreme position A, changes direction, moves to the other extreme position B, changes direction again and returns to O.
Alternatively, one oscillation is completed when the bob moves from one extreme position A to the other extreme position B and back to A.
The time taken for the pendulum to complete one oscillation is called its time period.
A piece of string about 150 cm long
A heavy metal ball or a small stone to act as the bob
A stopwatch or watch to measure time
A ruler to measure the length
1. Tie the bob to one end of the string.
2. Fix the other end of the string to a rigid support so that the length between the support and the bob is about 100 cm.
3. Let the bob come to rest in its mean position. The pendulum is now ready.
4. Gently pull the bob slightly to one side and release it without pushing. Make sure the string is taut when you release it.
5. Observe the pendulum oscillating back and forth.
6. Using the watch, measure the time taken for the pendulum to complete 10 oscillations.
7. Record the time in a table. Repeat this measurement three or four times for accuracy.
8. Calculate the time period by dividing the total time for 10 oscillations by 10.
Observations & Conclusion:
Length of the string = 100 cm
• The time period of the pendulum is nearly consistent across repeated measurements.
• This indicates that the time taken for one complete oscillation remains fairly constant for a pendulum of fixed length.
Conclusion: The pendulum's time period stays nearly constant because its length and the acceleration due to gravity at that location remain unchanged. This regularity makes pendulums useful for measuring time.
Think like a scientist:
When experimenting with pendulums, you can investigate questions such as:
How does the length of the pendulum affect its time period?
Do pendulums of different lengths have different time periods?
Does the mass of the bob affect the time period?
Conclusion from these tests: The time period of a simple pendulum depends on its length but not on the mass of the bob. At a given location, all pendulums of the same length have the same time period.
Dive deeper
Modern clocks measure time using repeating movements of different kinds. Instead of pendulums, many modern clocks use tiny vibrations of quartz crystals or the energy transitions of atoms. Early pendulum clocks could lose or gain about 10 seconds per day, but today's atomic clocks are vastly more accurate and can lose only about one second in millions of years. Scientists continue to improve clock accuracy for use in science, navigation and communications.
SI Unit of Time
• The standard unit of time in the International System of Units, or SI, is the second, symbolised as s.
• Larger units of time include the minute, with symbol min, and the hour, with symbol h.
Common conversions:
• 1 min = 60 s
• 1 h = 60 min = 3600 s
Rules for writing units: Unit names such as second, minute and hour start with a lower-case letter unless they begin a sentence. Their symbols, s, min and h, are always written in lower-case and remain singular. Do not put a full stop after a symbol unless it ends a sentence. Always leave a space between the number and the unit when writing time. Using abbreviations such as 'sec' for second or 'hrs' for hours is incorrect in formal usage.
Fascinating fact: The hole in the bowl of the Ghatika-yantra was designed so that the bowl took 24 minutes to fill and sink. This time interval was called a ghatika or ghati. A 24-hour day was divided into 60 equal ghatis. The ghati remained a standard unit of time in many places until the end of the 19th century.
Science and society: precision in time measurement
Sports: Timekeeping devices record events to one-hundredth or one-thousandth of a second to determine winners in races.
Medicine: Heart monitors such as electrocardiograms, or ECGs, measure heartbeat variations in milliseconds to help diagnose health issues.
Music: Digital recordings sample sound thousands of times per second for smooth playback.
Technology: Computers and smartphones process signals in microseconds and nanoseconds, enabling fast operation.
When we say that something is moving fast or slowly, we compare how far it moves in a certain amount of time.
For example, in a 100-metre race, all runners start together but soon spread out.
The runner who is ahead at a given moment has covered more distance in the same time and therefore has a higher average speed up to that moment.
Thus, the distance covered in a given time helps decide which object is moving faster or slower.
We say that the faster runner has a higher speed.
Speed is a measure of how fast an object is moving. It tells us the distance an object covers in a certain amount of time.
By comparing the distances moved by two or more objects in the same time, we can determine which object is moving faster.
The unit of time can be one second, one minute or one hour.
The distance covered by an object in a unit of time is called its speed.
The SI unit of speed is metre per second, written as m s⁻¹. For larger distances and times, speed is often given in kilometres per hour, written as km h⁻¹.
Speed = Total distance covered / Total time taken
Example 1:
Ravi's school is 5.2 km from his house. It took him 20 minutes to reach his school by bicycle. Calculate the speed of the bicycle in metres per second.
Solution:
Speed = Distance covered / Time taken
Distance = 5.2 km = 5.2 × 1000 m = 5200 m
Time = 20 minutes = 20 × 60 s = 1200 s
Speed = 5200 m / 1200 s ≈ 4.33 m s⁻¹
Answer: The speed of the bicycle is approximately 4.33 metres per second.
Activity: Comparing Train Speeds
To compare the speeds of different trains based on their timetable information, calculate the speed of each train using the timetable and compare the results:
Fastest train: The Superfast Train between Station G and Station H is the fastest, with a speed of 150 kilometres per hour.
Slowest train: The Passenger Train between Station A and Station B is the slowest, with a speed of 48 kilometres per hour.
The basic formula for speed is:
Speed = Total distance covered / Total time taken
The formula can be rearranged to find distance when speed and time are known:
Total distance covered = Speed × Total time taken
Similarly, we can find time when distance and speed are known:
Total time taken = Total distance covered / Speed
Example 2:
Priya is travelling to a nearby town in a car moving at a speed of 60 km/h. If it takes her 3 hours to reach the town, how far is the town?
Solution:
Distance = Speed × Time = 60 km h⁻¹ × 3 h = 180 km
Answer: The town is 180 km away.
Example 3:
A train is travelling at a speed of 80 km/h. How much time will it take to cover 240 km?
Solution:
Time = Distance / Speed = 240 km / 80 km h⁻¹ = 3 h
Answer: The train will take 3 hours to cover 240 km.
Average Speed
The speed calculated by dividing the total distance by the total time is the average speed.
An object may not move at the same speed throughout its journey. It may move more slowly at some times and faster at others.
When speed varies, the term speed is often used to mean average speed.
Speedometer: Vehicles such as scooters, motorbikes, cars and buses have an instrument called a speedometer. It shows the vehicle's speed in kilometres per hour (km h⁻¹).
Odometer: An odometer measures the total distance travelled by the vehicle in kilometres.
When an object moves along a straight line, the motion is called linear motion. Example: A train moving on a straight track between two stations.
This motion can be uniform, with constant speed, or non-uniform, with changing speed.
Uniform linear motion occurs when an object moves along a straight line with a constant, or unchanging, speed. It covers equal distances in equal intervals of time. Example: A car moving from one point to another at a constant speed.
Non-uniform Linear Motion
Non-uniform linear motion occurs when the speed of an object keeps changing while it moves along a straight line. It covers unequal distances in equal intervals of time. Example: A car whose speed varies while travelling from A to B to C.
Real-life note: Uniform motion is an ideal concept. In real life, an object rarely maintains a perfectly constant speed for a long time, so we often use average speed for practical purposes.
Case Study: Trains X and Y
Data are given for the distances travelled by two trains, X and Y, along straight tracks between 10:00 AM and 11:00 AM.
Solution:
• Train X covers equal distances in equal time intervals (such as 20 km in 10 minutes each), so it is in uniform linear motion.
• Train Y covers unequal distances in each equal time interval (such as 20 km followed by 15 km), so it is in non-uniform linear motion.
Thus, Train X moves uniformly while Train Y does not.
8. Terms to Remember
Sundial: A device that uses the Sun's shadow to indicate the time of day.
Water clock: A device that measures time by the flow of water into or out of a vessel.
Hourglass: A device that measures time by sand flowing between two bulbs.
Candle clock: A candle with markings that indicate time as the candle burns down.
Pendulum: A weight, or bob, hanging from a fixed point that swings back and forth and can be used to measure time.
Time period: The time taken for one complete oscillation of a pendulum.
Second: The SI unit of time, symbolised as s.
Speed: The distance covered by an object in a unit of time, measured in m s⁻¹ or km h⁻¹.
Speedometer: An instrument in vehicles that shows speed in km h⁻¹.
Odometer: An instrument in vehicles that measures the distance travelled in kilometres.
Linear motion: Motion along a straight line.
Uniform linear motion: Motion along a straight line at constant speed, covering equal distances in equal times.
Non-uniform linear motion: Motion along a straight line with changing speed, covering unequal distances in equal times.
Average speed: Total distance covered divided by the total time taken; used when speed varies.
Ghatika-yantra: A sinking-bowl water clock used in ancient India to measure time in ghatis.
Ghati: A traditional time unit equal to 24 minutes, measured by the Ghatika-yantra.
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