8.1 Measurement of Time

People have been interested in measuring time since ancient times. They noticed that many events in nature repeat at regular intervals.

Examples include:

• Rising and setting of the Sun
• Phases of the Moon
• Changing seasons

These repeating events helped people develop methods for measuring time.

How was time measured before clocks and watches?

People developed several devices to measure time, including:

• Sundials
• Water clocks
• Hourglasses
• Candle clocks

Samrat Yantra at Jantar Mantar, Jaipur. Wikimedia Commons photograph by Swapnil.Karambelkar. Check the Commons licence before reuse.

Water Clock

A water clock measures time using the flow of water. Water may flow out of a marked vessel, or a bowl with a small hole may gradually fill and sink.

Hourglass

An hourglass measures time by allowing sand to flow from one bulb to another.

Candle Clock

A candle clock has markings that indicate the passage of time as the candle burns.

Fascinating Fact: Samrat Yantra

The Samrat Yantra at Jantar Mantar in Jaipur is a huge stone sundial. Its shadow moves across a finely marked scale and can be used to measure time intervals.

Development of Mechanical Clocks

As civilisation advanced and people travelled longer distances, accurate measurement of time became increasingly important.

Mechanical clocks gradually developed using weights, gears and springs. The invention of the pendulum clock was a major development in accurate mechanical timekeeping.

8.1.1 A Simple Pendulum

A simple pendulum consists of a small metallic ball, called the bob, suspended from a rigid support by a thread.

Simple pendulum diagram. Wikimedia Commons. Public-domain diagram.

Important Terms

When a pendulum moves from its mean position to one extreme, then to the other extreme and back to the mean position, it completes one oscillation.

What do we learn?

• The time period is nearly the same for repeated measurements.
• The time period depends on the length of the pendulum.
• The mass of the bob does not affect the time period for a given length at a given location.

Modern Clocks and the SI Unit of Time

All clocks use some process that repeats regularly. Modern clocks may use vibrations of quartz crystals or specific atoms.

Remember that the symbols for second, minute and hour are written as s, min and h.

8.2 Slow or Fast?

When comparing two objects moving over the same distance, the object that takes less time is faster.

Another way to compare motion is to see how much distance an object covers in the same amount of time.

8.3 Speed

Speed tells us how much distance an object covers in unit time.

The SI unit of speed is metre per second (m/s).

Another commonly used unit is kilometre per hour (km/h).

Example

Activity 8.4: Finding the Speed of Trains

Train timetables can be used to find the distance and time taken between two stations and then calculate the average speed.

8.3.1 Relationship Between Speed, Distance and Time

Example 1

A bus travels at 50 km/h for 2 h.

Distance = 50 × 2 = 100 km

Example 2

A train travels at 90 km/h and covers 360 km.

Time = 360 ÷ 90 = 4 h

The speed calculated using total distance divided by total time is the average speed.

8.4 Uniform and Non-uniform Linear Motion

When an object moves along a straight line, its motion is called linear motion.

Train X and Train Y

Conclusion: Train X is in uniform linear motion because it covers equal distances in equal intervals of time.

In a Nutshell

• The time period of a pendulum is the time taken for one oscillation.
• The time period of a simple pendulum of a given length is constant at a particular place.
• The SI unit of time is the second (s).
• Speed is total distance divided by total time.
• The SI unit of speed is m/s.
• Uniform linear motion means equal distances in equal intervals of time.
• Non-uniform linear motion means unequal distances in equal intervals of time.
• Speedometer measures speed.
• Odometer measures distance travelled.

Let Us Enhance Our Learning

1. Calculate the speed of a car that travels 150 metres in 10 seconds. Express your answer in km/h.

Solution: Speed = 150 ÷ 10 = 15 m/s.

15 × 18/5 = 54 km/h.

2. A runner completes 400 metres in 50 seconds. Another runner completes the same distance in 45 seconds. Who has a greater speed and by how much?

Solution:

First runner = 400 ÷ 50 = 8 m/s.

Second runner = 400 ÷ 45 ≈ 8.89 m/s.

The second runner is faster by about 0.89 m/s.

3. A train travels at a speed of 25 m/s and covers a distance of 360 km. How much time does it take?

Solution: 360 km = 360,000 m.

Time = Distance ÷ Speed = 360000 ÷ 25 = 14400 s = 4 h.

4. A train travels 180 km in 3 h. Find its speed in:

(i) km/h

(ii) m/s

(iii) What distance will it travel in 4 h if it maintains the same speed throughout the journey?

Solution:

(i) Speed = 180 ÷ 3 = 60 km/h.

(ii) 60 × 5/18 = 16.67 m/s approximately.

(iii) Distance = 60 × 4 = 240 km.

5. The fastest galloping horse can reach the speed of approximately 18 m/s. How does this compare to the speed of a train moving at 72 km/h?

Solution: 72 km/h = 20 m/s.

The train is faster by 2 m/s.

6. Distinguish between uniform and non-uniform motion using the example of a car moving on a straight highway with no traffic and a car moving in city traffic.

Solution: A car moving at constant speed on a straight highway can show uniform motion. A car in city traffic repeatedly speeds up and slows down, so its motion is non-uniform.

7. Data for an object covering distances in different intervals of time are given in the following table. If the object is in uniform motion, fill in the gaps in the table.

Solution: The distances shown in the supplied textbook question indicate that the table should be completed according to the uniform-motion condition. The rate implied by the 10 s intervals must remain constant.

8. A car covers 60 km in the first hour, 70 km in the second hour, and 50 km in the third hour. Is the motion uniform? Justify your answer. Find the average speed of the car.

Solution: No. The car covers unequal distances in equal intervals of time, so its motion is non-uniform.

Average speed = Total distance ÷ Total time = 180 ÷ 3 = 60 km/h.

9. Which type of motion is more common in daily life— uniform or non-uniform? Provide three examples from your experience to support your answer.

Solution: Non-uniform motion is more common.

• A car moving through city traffic
• A bus stopping at different stops
• A cyclist speeding up and slowing down

10. Data for the motion of an object are given in the following table. State whether the speed of the object is uniform or non-uniform. Find the average speed.

Solution: The distances covered in equal time intervals are not equal, so the motion is non-uniform.

Average speed = Total distance ÷ Total time. Use the final distance and final time from the complete textbook table to calculate the average speed.

11. A vehicle moves along a straight line and covers a distance of 2 km. In the first 500 m, it moves with a speed of 10 m/s and in the next 500 m, it moves with a speed of 5 m/s. With what speed should it move the remaining distance so that the journey is complete in 200 s? What is the average speed of the vehicle for the entire journey?

Solution:

Total distance = 2000 m.

Remaining distance = 1000 m.

Time for first 500 m = 500 ÷ 10 = 50 s.

Time for next 500 m = 500 ÷ 5 = 100 s.

Time remaining = 200 − 150 = 50 s.

Required speed = 1000 ÷ 50 = 20 m/s.

Average speed = 2000 ÷ 200 = 10 m/s.

Exploratory Projects

1. Construct a floating bowl-type water clock.

Suggested approach: Use bowls with different sizes and holes and observe how the sinking time changes.

2. Design an activity for measuring the pulse rate.

Suggested approach: Count the number of pulse beats in one minute and compare the readings of different people.

3. Investigate differences in the time periods of a pendulum.

Suggested approach: Repeat the experiment carefully and reduce errors by keeping the length, release method and measurement technique consistent.

4. Investigate swings as pendulums.

Suggested approach: Measure the time for 10 oscillations, calculate the time period and repeat using different swing lengths.

Interdisciplinary Project

Gather the timings of the winners of the 100 m, 200 m and 400 m races for men and women in the last two Olympic Games. Calculate and compare their speeds.

Quick Revision