Observing the world around us reveals that everything is in constant change or motion. From the rising and setting of the sun to the swift movements of athletes, understanding and measuring both time and motion is fundamental. This chapter explores how we measure these aspects of the physical world, from ancient methods to modern precise techniques.

Consider the excitement of a race, where winners are determined by precise timing, even down to fractions of a second. This precision wasn't always available. How did people measure time and motion before modern clocks and devices?

8.1 Measurement Of Time

Humans have long been interested in tracking the passage of time. Early methods relied on observing predictable, repeating natural events.

• The cycle of the Sun's rising and setting defined a day.
• The phases of the Moon helped define longer periods.
• The changing seasons marked even longer cycles.

These natural cycles were used to create early calendars and measure large intervals of time. But people also needed ways to measure shorter intervals within a day, especially before the invention of mechanical clocks. This led to the development of various ingenious devices:

• Sundials: These devices used the changing position of a shadow cast by the Sun throughout the day to indicate the time.
• Water Clocks (Clepsydra): These measured time based on the controlled flow of water. One type involved water dripping out of a marked vessel, and another used a bowl with a small hole that gradually filled and sank when placed on the surface of water.
• Hourglasses (Sand Clocks): Time was measured by the amount of sand flowing from an upper bulb to a lower bulb through a narrow passage.
• Candle Clocks: Candles with markings were used; as the candle burned down, the markings indicated the passage of time.

Activity 8.1: Let Us Construct

A simple water clock can be constructed using a plastic bottle by cutting it in half, making a small hole in the cap, and inverting the top part into the bottom. Filling the top with water and marking the water level in the bottom section at regular intervals (e.g., every minute) using a watch allows you to measure time as the water drips.

Fascinating Fact: India has a rich history of timekeeping devices. The Samrat Yantra in Jaipur is a giant stone sundial capable of measuring time intervals as short as 2 seconds. Ancient texts like the Arthasastra describe shadow-based time measurement and water clocks. The Ghatika-yantra, a sinking bowl water clock, was widely used and even marked time with drums or gongs in public places.

The need for more accurate timekeeping, especially for navigation during long-distance travel, drove the development of mechanical clocks. A major turning point was the invention of the pendulum clock.

8.1.1 A Simple Pendulum

A simple pendulum is a basic device consisting of a small heavy object (called the bob) suspended by a light thread from a fixed point.

When the pendulum is at rest, the bob is in its lowest position, called the mean position. If the bob is pulled to one side and released, it swings back and forth. This back-and-forth movement is called oscillatory motion. Since this motion repeats itself after a fixed time interval, it is also a type of periodic motion.

One oscillation is defined as one complete swing of the bob. For example, starting from the mean position (O), moving to one extreme position (A), swinging through the mean position to the other extreme position (B), and finally returning back to the mean position (O).

The time taken by the pendulum to complete one such oscillation is called its time period.

Activity 8.2: Let Us Experiment

By setting up a simple pendulum of a specific length (e.g., 100 cm) and using a stopwatch, you can measure the time it takes for the pendulum to complete multiple oscillations (e.g., 10). The average time for one oscillation (Total time / Number of oscillations) gives the time period.

S.No.	Time taken for 10 oscillations (seconds)	Calculated Time period (seconds)
1.	(Recorded time)	(Time/10)
2.	(Recorded time)	(Time/10)
3.	(Recorded time)	(Time/10)

Repeating this measurement multiple times for the same pendulum length reveals a crucial property: the time period of a simple pendulum of a fixed length at a given location is nearly constant. This consistent periodicity made the pendulum a reliable mechanism for accurate timekeeping in clocks.

Think Like a Scientist: Following Galileo's footsteps, one could investigate how changing the pendulum's length or the bob's mass affects its time period. Experiments show that the time period depends on the length of the pendulum, with longer pendulums having longer time periods, but it is practically unaffected by the mass of the bob.

Modern clocks, while far more advanced, still rely on the principle of periodic, repeating processes. Quartz clocks use the extremely regular vibrations of a quartz crystal, while atomic clocks use the precise oscillations within atoms, achieving astonishing accuracy (losing only one second in millions of years).

8.1.2 SI Unit Of Time

The standard international unit for measuring time is the second. Its symbol is s.

Larger units of time commonly used are the minute (min) and the hour (h).

$1 \text{ minute} = 60 \text{ seconds}$

$1 \text{ hour} = 60 \text{ minutes}$

Writing Units Correctly: Unit names like second, minute, and hour start with a lowercase letter unless they begin a sentence. Their symbols (s, min, h) are also lowercase and used in the singular form (e.g., 10 s, not 10 secs). A space should be left between the number and the unit symbol (e.g., 5 min, not 5min).

Science and Society: The ability to measure time with high precision is critical in many modern fields. In sports, timekeeping devices can measure durations down to milliseconds or even microseconds to determine winners. Medical devices like ECGs measure tiny time variations in heartbeats. Digital technology, from audio recording to computing, relies on processing signals at extremely small time intervals (microseconds, nanoseconds). The relentless pursuit of greater accuracy in time measurement continues to benefit various aspects of society.

8.2 Slow Or Fast

Comparing how fast objects are moving is a common observation.

In a race over the same distance, the person who finishes first is considered the fastest. This is because they covered the same distance in less time than others.

Alternatively, if we compare the positions of runners at the same instant in time, the one who has covered more distance is moving faster.

These comparisons intuitively lead to the concept of speed – how much distance is covered in a certain amount of time.

8.3 Speed

The speed of an object quantifies how quickly it is moving. It is defined as the distance covered by the object in a unit interval of time (e.g., per second, per minute, or per hour).

To calculate the speed of an object, you divide the total distance it covers by the total time it takes to cover that distance:

$ \text{Speed} = \frac{\text{Total distance covered}}{\text{Total time taken}} $

The standard (SI) unit of speed is derived from the SI units of distance (metre, m) and time (second, s). Thus, the SI unit of speed is metres per second (m/s).

Another common unit for speed, especially for vehicles or longer distances, is kilometres per hour (km/h).

Example 8.1: If a bicycle travels 3.6 km (3600 m) in 15 minutes (15 x 60 = 900 s), its speed in m/s is:

$ \text{Speed} = \frac{3600 \text{ m}}{900 \text{ s}} = 4 \text{ m/s} $

8.3.1 Relationship Between Speed, Distance, And Time

The formula for speed can be rearranged to find distance or time if the other quantities are known:

• To find the total distance covered:

  $ \text{Total distance covered} = \text{Speed} \times \text{Total time taken} $

• To find the total time taken:

  $ \text{Total time taken} = \frac{\text{Total distance covered}}{\text{Speed}} $

Example 8.2: A bus travels at 50 km/h for 2 hours. The distance covered is:

$ \text{Distance} = 50 \text{ km/h} \times 2 \text{ h} = 100 \text{ km} $

Example 8.3: A train travels 360 km at a speed of 90 km/h. The time taken is:

$ \text{Time} = \frac{360 \text{ km}}{90 \text{ km/h}} = 4 \text{ h} $

Often, when we calculate speed using the total distance and total time for a journey where the speed might not have been constant, we are actually calculating the average speed. Throughout this chapter and book, the term 'speed' generally refers to 'average speed' unless specified otherwise.

Science and Society: Vehicles like cars and buses are equipped with a speedometer, which shows the instantaneous speed of the vehicle (usually in km/h). An odometer is another instrument in vehicles that measures the total distance covered (in km).

8.4 Uniform And Non-Uniform Linear Motion

Recall from previous learning that motion along a straight line is called linear motion.

When an object moves along a straight line at a constant speed (its speed does not change), its motion is called uniform linear motion. In this type of motion, the object covers equal distances in equal intervals of time.

When an object moves along a straight line, but its speed is changing (either increasing or decreasing), its motion is called non-uniform linear motion. In this type of motion, the object covers unequal distances in equal intervals of time.

Consider a train moving on a straight track between two stations. When it starts, it speeds up (non-uniform motion). It might travel at a constant speed for some part of the journey (uniform motion), and then slow down as it approaches the next station (non-uniform motion).

Looking at distance data collected at regular time intervals can help distinguish between uniform and non-uniform motion.

Time (AM)	Train X Position (km)	Train X Distance covered in 10 min (km)	Train Y Position (km)	Train Y Distance covered in 10 min (km)
10:00	0	0	0	0
10:10	20	20	20	20
10:20	40	20	35	15
10:30	60	20	50	15
10:40	80	20	75	25
10:50	100	20	95	20
11:00	120	20	120	25

In Table 8.3, Train X covers exactly 20 km every 10 minutes, showing it is in uniform linear motion. Train Y covers different distances (15 km, 25 km, 20 km, etc.) in the same 10-minute intervals, indicating it is in non-uniform linear motion.

In everyday life, truly uniform linear motion is rare; most motion involves changes in speed. Therefore, the concept of average speed is widely used to describe motion over a certain distance or time period.

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In a Nutshell:

• Historical timekeeping relied on repeating natural events and devices like sundials, water clocks, and hourglasses.
• The time period of a simple pendulum is the time taken to complete one oscillation. For a given length, it is nearly constant.
• Modern clocks use highly regular periodic processes, from quartz crystal vibrations to atomic oscillations, for precision.
• The SI unit of time is the second (s).
• Speed is the distance covered per unit time.
• $ \text{Speed} = \frac{\text{Total distance}}{\text{Total time}} $
• The SI unit of speed is m/s. Other common units include km/h.
• The formula can be rearranged to find distance ($ \text{Distance} = \text{Speed} \times \text{Time} $) or time ($ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $).
• 'Speed' often refers to 'average speed' for journeys with varying speeds.
• Uniform linear motion is movement along a straight line at constant speed (equal distances in equal times).
• Non-uniform linear motion is movement along a straight line with changing speed (unequal distances in equal times).
• Most motion in daily life is non-uniform.

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