Measurement of Time and Motion

CHAPTER 8: MEASUREMENT OF TIME AND MOTION

8.1 MEASUREMENT OF TIME

Historical Background of Time Measurement

Humans have been interested in tracking time for thousands of years. Early civilizations noticed that certain natural events repeat at fixed intervals:

Rising and setting of the Sun (defines a day)

Phases of the Moon

Changing seasons

These repeating cycles were used to create **calendars** and devices to measure time within a day.

Ancient Time-Measuring Devices

#### 1. **Sundial**

Works on the principle of shadow movement

A stick or object casts a shadow as the Sun moves across the sky during the day

Markings on the sundial show the time as the shadow position changes

Example: The **Samrat Yantra** at Jantar Mantar, Jaipur (built ~300 years ago) is the world's largest stone sundial with a height of 27 metres. Its shadow moves at 1 millimetre per second and can measure time intervals as short as 2 seconds.

#### 2. **Water Clock (Clepsydra)**

Two types:

**Type 1**: Water flows out from a vessel with time markings. As water drips out, the level drops and marks on the vessel show how much time has passed.

**Type 2**: A floating bowl with a small hole in the bottom. It gradually fills with water in a fixed time and sinks. Then it is lifted and floated again.

Used in ancient India (mentioned in Arthasastra by Kautilya, 2nd century BCE – 3rd century CE)

Problem: As water level drops, the flow rate decreases, making it less accurate

**Ghatika-yantra** (sinking bowl type) was first mentioned by Aryabhata (5th century CE) and used in Buddhist monasteries, royal palaces, and town squares. When the bowl sank, the time was announced by drums, conch shells, or gongs.

#### 3. **Hourglass (Sand Clock)**

Measures time by the flow of sand from one bulb to another through a narrow opening

Time period is fixed for the sand to flow completely from top bulb to bottom bulb

#### 4. **Candle Clock**

Candles with markings that indicate time passage as they burn

As the candle burns down, the markings show how much time has passed

Activity 8.1: Making a Simple Water Clock

**Materials Required:**

Used transparent plastic bottle (1/2 litre or larger) with cap

Drawing pin

Ink or food colour (optional)

Ruler

Watch

**Steps:**

1. Cut the plastic bottle into two halves roughly in the middle

2. Using a drawing pin, make a small hole in the cap of the bottle

3. Place the upper part of the bottle inverted over the lower half

4. Fill the upper part with water (add a few drops of ink/colour for visibility)

5. Water will start dripping into the lower part

6. Using a watch, mark the level of water after every one minute until all water drips down

7. Pour the water back into the top part

8. Every time the water level touches a marked line, one more minute has passed

The Pendulum Clock Revolution

**Galileo Galilei (1564-1642):** Italian scientist who observed a lamp swinging in a church ceiling. Using his pulse to measure time, he discovered that each swing of the lamp took the same time. He concluded that **the time taken to complete one oscillation is always the same for a pendulum of a given length**. This property is called **isochronism of pendulum**.

**Christiaan Huygens (1629-1695):** Dutch scientist who invented the **pendulum clock in 1656 and patented it in 1657**. This was inspired by Galileo's work. It marked a major breakthrough in mechanical timekeeping. Huygens' early pendulum clocks could gain or lose 10 seconds each day.

8.1.1 Simple Pendulum

#### Definition and Components

A **simple pendulum** consists of:

A small metallic ball called the **bob**

A long thread suspending the bob

A rigid support from which the thread hangs

#### Motion of a Pendulum

**Mean Position:** The position where the pendulum is at rest (vertical position)

**Extreme Positions:** The positions on either side (A and B) where the bob momentarily stops before changing direction

**Oscillatory Motion:** The back-and-forth motion of the pendulum. It is **periodic in nature** because it repeats the same path after a fixed interval of time.

#### Oscillation

One complete **oscillation** is when:

The bob starts from mean position O

Moves to extreme position A

Changes direction and moves to extreme position B

Changes direction again and returns to O

OR

The bob moves from one extreme position A to another extreme position B and back to A

#### Time Period

**Time Period (T):** The time taken by a pendulum to complete one oscillation. It is measured in seconds.

Activity 8.2: Measuring the Time Period of a Pendulum

**Materials Required:**

String (~150 cm long)

Heavy metal ball with hook or a stone (bob)

Stopwatch or watch

Ruler

**Steps:**

1. Tie the bob at one end of the string

2. Fix the other end of the string to a rigid support such that the length of string between support and bob is around 100 cm

3. Wait for the bob to come to rest (mean position)

4. Gently hold the bob, move it slightly to one side, and release it (do not push)

5. Ensure the string remains taut during motion

6. Using a watch, measure the time taken for the pendulum to complete 10 oscillations

7. Record the time in a table

8. Repeat the activity 3-4 times

9. Divide the time for 10 oscillations by 10 to get the time period

**Expected Observation:** The time period of the pendulum is almost the same every time.

**Important Facts About Simple Pendulum:**

**Time period depends on length:** A longer pendulum has a longer time period

**Time period is independent of bob's mass:** Whether the bob is light or heavy, the time period remains the same for a given length

**All pendulums of the same length have the same time period at a given location**

**Time period is constant at a place:** This property is used in clocks to measure time accurately

Modern Time Measurement

**Quartz Clocks:** Use vibrations from quartz crystals to measure time

**Atomic Clocks:** Use vibrations from specific atoms to measure time

So precise that they lose only one second in millions of years

Much more accurate than early pendulum clocks

All clocks (old or modern) are based on a process that repeats continuously and can mark equal intervals of time.

8.1.2 SI Unit of Time

**The SI unit of time is the second (s)**

**Important Relations:**

60 seconds (s) = 1 minute (min)

60 minutes (min) = 1 hour (h)

**Writing Rules for Units:**

Units (second, minute, hour) begin with lowercase letter except at the beginning of a sentence

Symbols (s, min, h) are written in lowercase and singular form

No full stop after the symbol (except at end of sentence)

Leave a space between the number and the unit (example: 5 s, not 5s)

Writing 'sec' for second and 'hrs' for hour is INCORRECT

**Historical Time Unit in India:**

The **Ghatika-yantra** took 24 minutes to fill and sink. This time unit was called **ghatika** or **ghati**. A 24-hour day was divided into 60 equal ghatis. This standard unit of time measurement continued until the end of the 19th century.

Importance of Precise Time Measurement in Modern Life

**In Sports:** Sports timekeeping devices can record events down to one-hundredth or even one-thousandth of a second (millisecond) to determine race winners

**In Medicine:**

Electrocardiogram (ECG) machines measure millisecond variations in heartbeats to detect health issues

Heart rate monitoring requires precision timing

**In Music:** Digital recordings capture sound thousands of times per second for smooth playback

**In Technology:**

Smartphones and computers process signals in microseconds (one-millionth of a second)

This allows them to operate very fast and efficiently

**In Space Exploration and Advanced Science:** Scientists develop even more precise time-measuring tools for research

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8.2 SLOW OR FAST - CONCEPT OF SPEED

What Determines "Faster" or "Slower"?

When multiple objects travel together:

The object that **covers more distance in the same time** is moving faster

The object that **covers less distance in the same time** is moving slower

**Example:** In a 100-meter race:

All runners start together at the same time

The runner who reaches the finish line first has covered the maximum distance in the minimum time

This runner is the fastest

Key Principle

**The distances moved by objects in a given interval of time decide which one is faster or slower.**

When we say something is moving fast, we mean it has **high speed**. When we say something is moving slow, it has **low speed**.

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8.3 SPEED

Definition of Speed

**Speed** is the distance covered by an object in a unit time.

It tells us how much distance an object travels in one unit of time (1 second, 1 minute, or 1 hour).

Formula for Speed

**Speed = Total Distance Covered / Total Time Taken**

Or:

**Speed = Distance / Time**

SI Unit of Speed

Since Speed = Distance / Time

And SI unit of distance = metre (m)

And SI unit of time = second (s)

**SI unit of speed = metre per second (m/s)**

This is written as: **m/s** or **m·s⁻¹**

Other Units of Speed

**Kilometre per hour (km/h):**

Used when distance is in kilometres and time is in hours

Common unit for vehicle speed

Example: A car traveling at 60 km/h

Example 8.1: Calculating Speed

**Problem:** Swati's school is 3.6 km from her house. It took her 15 minutes to reach school by bicycle. Calculate the speed of the bicycle in m/s.

**Solution:**

Speed = Distance / Time

= 3.6 km / 15 min

Convert to SI units:

3.6 km = 3.6 × 1000 m = 3600 m

15 min = 15 × 60 s = 900 s

Speed = 3600 m / 900 s = 4 m/s

**Answer:** The speed of the bicycle is 4 m/s

Activity 8.3: Understanding Time Measurement

**Observation:** When looking at a wall clock with minute and second hands:

The smallest interval of time you can measure is **one second**

This is because the clock hands move in second intervals

Activity 8.4: Calculating Speed of Trains

**Steps:**

1. Look up a railway timetable on the internet

2. Identify a train stopping at the nearest railway station

3. Find the next station where the train stops and the distance to that station

4. Note the departure time from your station and arrival time at the next station

5. Calculate time taken = Arrival time - Departure time

6. Calculate speed = Distance / Time (in km/h)

7. Repeat for 4-5 different types of trains (Passenger, Express, Superfast)

**Comparison:** The train that covers the maximum distance in unit time has the highest speed and is the fastest train.

**Observation:** Different types of trains have different speeds:

Passenger trains: Lower speed

Express trains: Medium speed

Superfast trains: Highest speed

8.3.1 Relationship Between Speed, Distance, and Time

There are three important relationships:

#### 1. **Calculate Speed**

**Speed = Distance / Time**

#### 2. **Calculate Distance**

**Distance = Speed × Time**

If you know the speed and time, you can find the distance covered.

#### 3. **Calculate Time**

**Time = Distance / Speed**

If you know the distance and speed, you can find the time taken.

Example 8.2: Calculating Distance

**Problem:** Raghav is going to a neighbouring city in a bus moving at 50 km/h. If it takes him 2 hours to reach the city, how far is the city?

**Solution:**

Distance = Speed × Time

= 50 km/h × 2 h

= 100 km

**Answer:** The city is 100 km away.

Example 8.3: Calculating Time

**Problem:** A train is travelling at 90 km/h. How much time will it take to cover 360 km?

**Solution:**

Time = Distance / Speed

= 360 km / 90 km/h

= 4 hours

**Answer:** The train will take 4 hours to cover 360 km.

Important Note: Average Speed

In all the examples above, we calculated **Average Speed** using:

**Average Speed = Total Distance Covered / Total Time Taken**

This is because:

Objects usually do not travel at the same speed throughout the journey

They may speed up, slow down, or stop at various points

The calculated speed is the average of all these speed variations

**Example:** A car journey where:

First 30 minutes: traveling at 60 km/h

Next 30 minutes: traveling at 40 km/h

The average speed for the 1-hour journey is the total distance divided by 1 hour, not simply the average of 60 and 40

In this textbook, when we use the term **"speed,"** we mean **"average speed"** unless otherwise stated.

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8.4 UNIFORM AND NON-UNIFORM LINEAR MOTION

Linear Motion Review

**Linear Motion:** Motion of an object along a straight line.

Reference: Studied in Grade 6 Science textbook 'Curiosity'

Example: Train Motion Between Two Stations

Consider a train traveling on a straight track between two railway stations A and D:

**At Station A:** Train starts with slow speed

**Between A and B:** Train gradually increases speed

**Between B and C:** Train moves at a constant (unchanging) speed

**Between C and D:** Train slows down

**At Station D:** Train comes to a complete halt

Uniform Linear Motion

**Definition:** Motion in a straight line where an object covers equal distances in equal intervals of time (at constant speed).

**Characteristics:**

Speed remains **constant** (does not change)

The object covers the same distance in each second, minute, or hour

Acceleration is **zero** (no change in velocity)

Graph of distance vs. time is a **straight line** (if time is on x-axis and distance on y-axis)

**Examples:**

A car moving at a constant 60 km/h on a highway

A train moving at constant speed between stations B and C

A person walking at a steady pace on a straight road

A cyclist maintaining the same speed on a flat road

Non-uniform Linear Motion

**Definition:** Motion in a straight line where an object covers **unequal distances in equal intervals of time** (speed keeps changing).

**Characteristics:**

Speed is **not constant** (keeps changing)

The object covers different distances in different seconds, minutes, or hours

**Acceleration is present** (change in velocity)

Graph of distance vs. time is a **curve** (not a straight line)

**Examples:**

A train starting from a station and gradually increasing speed

A car braking as it approaches a red light (decreasing speed)

A runner in a marathon who alternates between fast and slow speeds

A ball rolling down a slope (speed keeps increasing due to gravity)

A vehicle accelerating from 0 to 60 km/h

Comparing Uniform and Non-Uniform Motion

| Feature | Uniform Motion | Non-Uniform Motion |

|---------|---|---|

| **Speed** | Constant (unchanging) | Changes with time |

| **Distance covered in equal time** | Equal | Unequal |

| **Acceleration** | Zero | Present |

| **Distance-time graph** | Straight line | Curve |

| **Real-life examples** | Rare in real life; maintained briefly | Very common in everyday life |

Indian Real-Life Examples

**Uniform Motion:**

An auto-rickshaw moving at constant speed on a straight highway at night with no traffic

A train moving between two signals at constant speed

An escalator in a shopping mall (moving at constant speed)

**Non-Uniform Motion:**

An auto-rickshaw in city traffic that constantly speeds up and slows down

A train starting from a station and gradually picking up speed

A motorcycle accelerating from a red light

A cricket ball that is hit by a batsman and gradually slows down as it moves across the field

A person riding a bicycle uphill (speed decreases) and then downhill (speed increases)

Diagrams to Draw:

**Diagram 1: Distance-Time Graph for Uniform Motion**

Draw a coordinate system with Time (seconds) on x-axis and Distance (metres) on y-axis

Draw a straight line starting from origin at an angle

Label it "Uniform Motion - Straight Line"

Explanation: For every equal time interval, the distance increases by the same amount

**Diagram 2: Distance-Time Graph for Non-Uniform Motion**

Draw a coordinate system with Time (seconds) on x-axis and Distance (metres) on y-axis

Draw a curve (not a straight line) that increases gradually and then more steeply

Label it "Non-Uniform Motion - Curved Line"

Explanation: The slope of the curve changes, showing speed is changing

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KEY FORMULAS AND RELATIONSHIPS

**Speed = Distance / Time**

**Distance = Speed × Time**

**Time = Distance / Speed**

**Time Period of Pendulum (T)** = Time for 10 oscillations / 10

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IMPORTANT HISTORICAL FACTS

1. **Kautilya (2nd-3rd century BCE):** Described shadow-based time measurement in Arthasastra

2. **Varahamihira (530 CE):** Gave accurate expression for time using shadow of a vertical stick

3. **Aryabhata (5th century CE):** First mentioned the sinking bowl water clock (Ghatika-yantra)

4. **Christiaan Huygens (1657):** Invented the pendulum clock, revolutionizing timekeeping

5. **Galileo Galilei (1564-1642):** Discovered that pendulum time period is constant for a given length

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FREQUENTLY USED TERMS

**Bob:** The metallic ball in a simple pendulum

**Oscillation:** One complete back-and-forth motion of a pendulum

**Mean Position:** The position where the pendulum is at rest

**Extreme Position:** The farthest points on either side where the pendulum momentarily stops

**Time Period:** Time taken for one complete oscillation

**Speed:** Distance covered per unit time

**Uniform Motion:** Motion at constant speed in a straight line

**Non-Uniform Motion:** Motion with changing speed in a straight line

**Linear Motion:** Motion along a straight line

**Periodic Motion:** Motion that repeats after a fixed interval of time

**Average Speed:** Total distance divided by total time

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STUDENT CHECKLIST FOR EXAM PREPARATION

✓ Can explain how ancient people measured time

✓ Can describe 4 ancient time-measuring devices with examples

✓ Can construct a simple water clock (Activity 8.1)

✓ Understand Galileo's pendulum discovery

✓ Know who invented the pendulum clock and when

✓ Can define and identify parts of a simple pendulum

✓ Can conduct Activity 8.2 to measure time period

✓ Know the relationship between pendulum length and time period

✓ Understand that time period is independent of bob's mass

✓ Can write SI unit of time and conversion factors

✓ Understand the concept of speed

✓ Can apply the formula: Speed = Distance / Time

✓ Can solve problems using distance, speed, and time formulas

✓ Understand the difference between uniform and non-uniform motion

✓ Can identify real-life examples of uniform and non-uniform motion

✓ Know the importance of precise time measurement in modern life

✓ Can analyze railway timetables and calculate train speeds (Activity 8.4)