In previous classes, you were introduced to different types of **motion**, including motion along a straight line (rectilinear), circular motion, and periodic motion. This chapter delves deeper into understanding motion, specifically focusing on how to describe and measure it using the concepts of time and speed.

Recall the types of motion:

• Rectilinear Motion: Movement along a straight path (e.g., a car on a straight road).
• Circular Motion: Movement along a circular path (e.g., a point on a rotating fan blade).
• Periodic Motion: Motion that repeats itself after fixed intervals of time (e.g., the swing of a pendulum).

Table 13.1: Examples of different types of motion (Example Structure):

Example of motion	Type of motion (Along a straight line/circular/periodic)
Soldiers in a march past	Along a straight line
Bullock cart moving on a straight road	Along a straight line
Hands of an athlete in a race	Periodic (swinging back and forth)
Pedal of a bicycle in motion	Circular
Motion of the Earth around the Sun	Circular (also periodic)
Motion of a swing	Periodic (also oscillatory)
Motion of a pendulum	Periodic (oscillatory)

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Slow Or Fast

It's a common observation that some objects move faster than others. Even the same object might move at different speeds at different times. We intuitively categorize motion as **slow** or **fast** by comparing how much distance is covered in a certain amount of time.

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Activity 13.1

Observing the positions of multiple vehicles moving in the same direction on a road at two different moments in time (Fig. 13.1 and Fig. 13.2). By comparing the distance each vehicle has moved during the time interval between the two observations, we can determine which vehicle covered the most distance and is therefore moving the fastest, and which covered the least distance and is moving the slowest.

This observation leads to the understanding that the **distance moved by an object in a given time interval** is a way to quantify whether its motion is fast or slow.

Speed

The term "**speed**" is used to describe how fast an object is moving. A higher speed means an object covers a greater distance in the same amount of time, or the same distance in a shorter amount of time.

To quantitatively compare the fastness or slowness of motion, we calculate the distance an object covers in a **unit time** (e.g., per second, per minute, per hour). The distance covered by an object in a unit time is defined as its **speed**.

The formula for calculating speed is:

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

When we say a car has a speed of 50 kilometres per hour (km/h), it means it would cover a distance of 50 km if it maintained that speed for one hour. Often, the speed of a moving object is not constant; it may speed up or slow down. In such cases, the calculated speed (Total distance / Total time) represents the **average speed** over the entire journey. Unless specified otherwise, when we use the term "speed" in this context, we refer to the average speed.

Motion along a straight line with a constant speed is called uniform motion. If the speed keeps changing, it is called non-uniform motion.

Measurement Of Time

To determine the speed of an object, we need to measure both the distance covered and the **time taken**. We already know how to measure distance (Chapter 10, Class VI), but accurately measuring time requires specific devices.

In ancient times, people relied on natural events that repeat at regular intervals to keep track of time. Examples include:

• A **day**: The time between one sunrise and the next.
• A **month**: Measured from one new moon to the next.
• A **year**: The time taken by the Earth to complete one revolution around the Sun.

For measuring shorter intervals of time, devices like clocks and watches are used. These devices often rely on a **periodic motion** – a motion that repeats itself after regular intervals of time.

One of the most famous examples of periodic motion used in timekeeping is that of a **simple pendulum**.

A simple pendulum consists of a small object (called the **bob**, usually a metallic ball or stone piece) suspended from a rigid support by a thread or string. When displaced from its resting position (mean position) and released, the pendulum swings back and forth. This back-and-forth motion is an example of periodic or oscillatory motion.

An **oscillation** is completed when the pendulum bob, starting from a point (e.g., mean position O), moves to one extreme (A), then to the other extreme (B), and finally returns to the starting point O. Alternatively, it can be defined as the movement from one extreme position (A) to the other extreme (B) and back to the first extreme position (A).

The **time period** of a simple pendulum is the time it takes to complete one full oscillation. A key property of a simple pendulum with a fixed length is that its time period is **constant**, regardless of small changes in the initial displacement (how far it is pulled aside).

This property was famously observed by **Galileo Galilei**, leading to the development of pendulum clocks, which were a significant improvement in time measurement accuracy compared to earlier devices.

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Activity 13.2

Setting up a simple pendulum (thread length about 1 meter, with a bob) and measuring the time taken for a certain number of oscillations (e.g., 20 oscillations) using a stopwatch or a clock. The time period (time for one oscillation) is calculated by dividing the total time taken by the number of oscillations. Repeating the measurement several times and with slightly different initial displacements helps confirm that the time period is approximately constant for a given pendulum length.

Table 13.2: Recording Time Period of a Simple Pendulum (Example Structure):

S.No.	Time taken for 20 oscillations (s)	Time period (s) (Time taken / 20)
1.	...	...
2.	...	...
3.	...	...

Modern clocks and watches use electric circuits with vibrating quartz crystals for timekeeping, known as **quartz clocks**. These are highly accurate compared to older mechanical clocks.

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Units of Time and Speed:

The basic unit of time in the International System of Units (SI units) is the **second (s)**. Larger units include the minute (min) and the hour (h), with standard relationships (1 min = 60 s, 1 h = 60 min = 3600 s). Time intervals can range from fractions of a second (microseconds, nanoseconds used in scientific research and sports timing) to centuries and millenniums for historical periods, or even billions of years for cosmic timescales.

The basic unit of speed is derived from the units of distance and time. Since Speed = Distance / Time, the basic unit of speed is **metre per second (m/s)**. Other common units include metres per minute (m/min) and kilometers per hour (km/h).

Units are typically written in singular form (e.g., 10 km, 5 s, 2 m/s).

Before pendulum clocks, various other devices were used to measure time, such as **sundials** (measuring time based on the position of the sun's shadow), **water clocks** (measuring time based on the flow of water), and **sand clocks** (like hourglasses, measuring time based on the flow of sand).

Measuring Speed

To calculate the **speed** of an object, we need to measure the **distance** it travels and the **time** it takes to cover that distance. We can then use the formula: Speed = Total distance covered / Total time taken.

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Activity 13.3

Measuring the speed of a rolling ball. Draw a line on the ground. Roll a ball gently towards the line. Note the time when the ball crosses the line (start time) and when it comes to a complete stop (end time). Measure the distance from the line to where the ball stopped. The speed of the ball over this distance can be calculated by dividing the distance moved by the time taken to come to rest from the line.

Table 13.3: Recording Distance, Time, and Speed of a moving ball (Example Structure):

Name of the group	Distance moved by the ball (m)	Time taken (s)	Speed = Distance/Time taken (m/s)
Group A	...	...	...
Group B	...	...	...
...	...	...	...

Once the speed of an object is known, we can also use it to calculate other values:

• Distance covered = Speed $\times$ Time
• Time taken = Distance / Speed

Vehicles like cars, scooters, and buses have instruments on their dashboard to provide information about speed and distance travelled. A **speedometer** measures and displays the instantaneous speed of the vehicle, usually in km/h. An **odometer** measures and records the total distance covered by the vehicle in kilometers.

Table 13.4: Fastest speeds of some animals (Example):

S. No.	Name of the object	Speed in km/h	Speed in m/s (Calculated)
1.	Falcon	320	≈ 88.9
2.	Cheetah	112	≈ 31.1
3.	Blue fish	40 – 46	≈ 11.1 – 12.8
4.	Rabbit	56	≈ 15.6
5.	Squirrel	19	≈ 5.3
6.	Domestic mouse	11	≈ 3.1
7.	Human	40	≈ 11.1
8.	Giant tortoise	0.27	≈ 0.075
9.	Snail	0.05	≈ 0.014

Table 13.5: Odometer reading and distance from start point over time (Example Structure):

Time (AM)	Odometer reading (km)	Distance from the starting point (km)
8:00 AM	36540.0	0
8:30 AM	36560.0	20
9:00 AM	36580.0	40
9:30 AM	36600.0	60
10:00 AM	36620.0	80

Distance-Time Graph

Information about motion can be presented visually using graphs. A **distance-time graph** is a type of line graph that shows how the distance covered by an object changes over time.

Graphs are plotted on graph paper, which has a grid of perpendicular lines. Two perpendicular lines are drawn to represent axes:

• The **x-axis** (horizontal line) is typically used to represent **time**.
• The **y-axis** (vertical line) is typically used to represent **distance**.

The point where the x-axis and y-axis intersect is called the **origin (O)**. Positive values are marked along OX (right from origin) and OY (up from origin).

Table 13.6: Motion of a car (Example Data for Graphing):

S. No.	Time (min.)	Distance (km)
1.	0	0
2.	1	1
3.	2	2
4.	3	3
5.	4	4
6.	5	5

Steps for Plotting a Distance-Time Graph:

1. Draw and label the x-axis (Time) and y-axis (Distance).
2. Choose appropriate **scales** for both axes. The scale should be chosen based on the range of data values (highest and lowest) and the size of the graph paper to effectively utilize the space. For example, if covering 80 km, a scale like 10 km = 1 cm might be suitable. If measuring time up to 1 hour (60 min), a scale like 6 min = 1 cm might work.
3. Mark the values for time on the x-axis and distance on the y-axis according to the chosen scales.
4. Plot points on the graph paper corresponding to each pair of time and distance values from the data table. For example, at time 0, distance is 0 (origin). At time 1 min, distance is 1 km; find 1 min on the x-axis and 1 km on the y-axis, and mark the point where lines from these values intersect.
5. Join all the plotted points with a line. This line is the distance-time graph.

If the distance-time graph for an object's motion is a **straight line**, it indicates that the object is moving with a **constant speed** (uniform motion). If the speed changes, the graph will be a curved line.

Distance-time graphs are useful because they provide information about motion at any point in time, not just the specific intervals given in a table. For example, from the graph of the bus journey (Fig. 13.14), one can find the distance covered at a specific time like 8:15 AM by finding the point on the graph corresponding to that time and reading the distance on the y-axis.

The speed of the object can also be calculated from the graph. For an object moving at a constant speed, the slope of the distance-time graph (change in distance / change in time) represents its speed.

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