NCERT Science Notes - Class 9
Chapter 7 - Motion

Welcome to AJs Chalo Seekhen. This webpage is dedicated to Class 9 | Science | Chapter 7 - Motion. In this chapter, students delve into the concept of motion, a fundamental aspect of physics. They explore different types of motion such as uniform and non-uniform motion. The chapter introduces important concepts like speed, velocity, and acceleration, explaining their differences and how to measure them. Students learn to represent motion graphically, using distance-time and velocity-time graphs. The chapter also covers equations of motion and how they apply to everyday situations. Understanding motion helps students grasp the principles governing the movement of objects, forming a basis for more complex topics in physics. 🚀📘

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NCERT Science Notes - Class 9
Chapter 7 - Motion

In our daily lives, we encounter various objects in different states of motion. Motion can be described as the change in position of an object with respect to time. Here are some examples of motion:

• Birds fly in the sky.
• Fish swim in water.
• Blood flows through veins and arteries.
• Cars move on roads.

Perception of Motion

• Direct Motion: We often perceive motion directly when an object's position changes relative to a stationary background.
• Indirect Motion: Sometimes, we infer motion through indirect evidence. For instance:
  • The movement of dust or leaves can indicate the motion of air.

Causes of Natural Phenomena

Sunrise, Sunset, and Changing Seasons

The phenomena of sunrise, sunset, and changing seasons are primarily caused by the motion of the Earth:

• Earth's Rotation: The Earth rotates on its axis, causing the sun to appear to rise in the east and set in the west.
• Earth's Revolution: The Earth's orbit around the sun leads to seasonal changes as different parts of the Earth receive varying amounts of sunlight throughout the year.
  
  

• The Earth's motion is relatively constant and occurs at a high speed (approximately 1670 kilometers/hour at the equator).
• We do not feel this motion because we are moving along with the Earth and everything around us in a uniform manner, similar to how passengers in a moving vehicle do not feel the motion as they would if they were standing still.

Relative Motion

Motion is relative, meaning an object can appear to be in motion for one observer and at rest for another. 

Example of Relative Motion:

• Inside a Moving Bus:
  • Passengers inside a moving bus see their fellow passengers as stationary.
  • The roadside trees appear to move backward from the perspective of the bus passengers.
• Outside Observer:
  • A person standing on the roadside sees both the bus and its passengers moving forward.

Conclusion on Observations

These observations illustrate the concept of relative motion:

• Motion is not absolute; it depends on the observer's frame of reference.
• Understanding this concept is crucial for studying motion and its various types.

Most motions are complex and can be classified into different categories:

1. Linear Motion: Movement in a straight line.
2. Circular Motion: Movement in a circular path.
3. Rotational Motion: Spinning around an axis.
4. Vibrational Motion: Rapid back-and-forth movements.

Activity 7.1: Classroom Walls

• Discussion Prompt: Are the walls of your classroom at rest or in motion?
  • Explanation: The classroom walls are typically at rest relative to the classroom and the Earth. However, in the context of the Earth's rotation and revolution, they are in motion along with the Earth.

Activity 7.2: Perception of Train Motion

• Experience Sharing Prompt: Have you ever felt that the train you are sitting in appears to move while it is at rest?
  • Discussion Points:
    • This phenomenon can be attributed to relative motion.
    • When the train starts moving, the passengers may feel a jolt, while the objects inside the train appear to be at rest until they are in motion relative to the train.

Think and Act

Key Concepts:

1. Erratic Motion:
   • Defined as unpredictable and uncontrolled movement of objects.
   • Examples include:
     • Flooded River: Rapid and unpredictable water flow can cause danger.
     • Hurricane: Strong winds and erratic patterns can lead to destruction.
     • Tsunami: Sudden, large ocean waves resulting from underwater disturbances.
2. Controlled Motion:
   • Defined as organized and predictable movement of objects.
   • Example:
     • Hydro-Electric Power Generation: Utilizes controlled water flow to generate electricity, benefiting human needs.

• Do you feel the necessity to study the erratic motion of some objects and learn to control them?
  • Yes, understanding erratic motion can help mitigate dangers and harness energy efficiently.

• Studying both erratic and controlled motion is essential for safety and technological advancement.

7.1 - Describing Motion

• Reference Point:
• An object’s location is specified in relation to a reference point (origin).
• Example: A school is 2 km north of a railway station. Here, the railway station is the reference point.

7.1.1 - Motion Along a Straight Line

• Type of Motion:
  • The simplest form of motion is along a straight path.
• Example of Motion:
  • An object moves from point O (reference point) through points C, B, to A, and back to C.
  • Path Length Calculation:
    • From O to A: 60 km
    • From A to C: 35 km
    • Total Path Length: OA + AC = 60 km + 35 km = 95 km (Distance)

• Distance:
  • Defined as the total length of the path traveled, irrespective of direction.
  • Example: Distance from O to A and back to B is 85 km (60 km + 25 km).
• Displacement:
  • Defined as the shortest distance from the initial position to the final position.
  • Calculation:
    • For the journey from O to C via A:
      • Distance = 60 km (O to A) + 35 km (A to C) = 95 km
      • Displacement = Direct distance from O to C = 35 km (shortest path).

• Magnitude of Displacement vs. Distance:
  • The magnitude of displacement can be less than the total distance traveled.
  • Example:
    • From O to A (60 km): Distance = 60 km, Displacement = 60 km.
    • From O to A and back to B:
      • Distance = 60 km + 25 km = 85 km, Displacement = 35 km.
  • Zero Displacement Example:
    • If the object returns to the original position (O), displacement = 0, but the total distance traveled = 120 km (60 km + 60 km).

Distance and Displacement are two distinct physical quantities used to describe motion:

• Distance: Total path length, always positive.
• Displacement: Shortest path between initial and final positions, can be zero.

Activity 7.3: Measuring Distance and Displacement

Instructions

1. Materials Needed:
   • A metre scale
   • A long rope
2. Procedure:
   • Walk from one corner of a basketball court to the opposite corner along the sides of the court.
   • Use the metre scale to measure the distance you covered while walking.
3. Measurement:
   • Distance Covered: Measure the total length of the path walked along the sides of the basketball court.
   • Magnitude of Displacement: Calculate the straight-line distance from the starting corner to the opposite corner.
     
     

• Difference Noticed:
  • The distance covered will be greater than the magnitude of the displacement, as displacement measures the shortest path between two points, while distance accounts for the actual path taken.

Activity 7.4: Odometer Reading and Displacement Calculation

Instructions

1. Odometer Definition:
   • An odometer is a device fitted in automobiles to show the distance traveled.
2. Scenario:
   • A car travels from Bhubaneshwar to New Delhi.
   • The odometer reading difference is 1850 km.
3. Calculation of Displacement:
   • To find the magnitude of the displacement between Bhubaneshwar and New Delhi:
     • Use a Road Map of India to determine the straight-line distance (geodesic) between the two cities.

• Magnitude of Displacement:
  • The displacement value may differ from the odometer reading since the odometer measures the distance traveled along the roads, which can be longer than the straight-line distance between the two cities.

7.1.2 - UNIFORM MOTION AND NONUNIFORM MOTION

Uniform Motion:

• Definition:
  • Motion in which an object covers equal distances in equal intervals of time.
• Example:
  • An object traveling:
    • 5 m in the first second
    • 5 m in the second second
    • 5 m in the third second
    • 5 m in the fourth second
  • In this case, the object consistently covers 5 m every second, indicating uniform motion.

• Distances covered in each time interval are equal.
• The time intervals should be small to maintain the definition of uniform motion.

• Definition:
  • Motion in which an object covers unequal distances in equal intervals of time.
• Examples:
  • A car moving on a crowded street, where it frequently stops and accelerates.
  • A person jogging in a park, varying their pace throughout the run.

• Distances covered in each time interval are not equal.
• Motion is affected by external factors such as obstacles, speed variations, or changes in direction.

• Uniform Motion: Equal distance in equal time intervals (e.g., 5 m every second).
• Non-Uniform Motion: Unequal distances in equal time intervals (e.g., car in traffic, jogging with varied speed).

Activity: Determine Uniform or Non-Uniform Motion of Objects A and B

Objective: To analyze the motion of two objects, A and B, based on the given distance and time data, and determine whether their motion is uniform or non-uniform.

Data: The data regarding the distance traveled by two different objects (A and B) at specific times is given in Table 7.1.

Table 7.1: Distance Traveled by Objects A and B Over Time

7.2 - Measuring the Rate of Motion

Activity 7.6

• Objective: Measure the time it takes you to walk from your house to your bus stop or school.
• Assumption: If your average walking speed is 4 km/h, estimate the distance to the bus stop or school.

Activity 7.7

• Objective: Understand the time delay between seeing lightning and hearing thunder.
• Observation: When it is cloudy, you may frequently observe thunder and lightning. The sound of thunder takes time to reach you after you see the lightning.
• Questions:
  • Can you explain why this happens?
  • Measure the time interval using a digital wristwatch or stopwatch.
  • Calculate the distance to the nearest point of lightning using the speed of sound in air (346 m/s).

$$\text{Distance} = \text{Speed} \times \text{Time}$$

7.3 - Rate of Change of Velocity

Activity 7.8: Identifying Types of Acceleration in Everyday Life

In your daily life, you can observe several motions that fall into different categories of acceleration. Here’s an example for each type:

(a) Acceleration is in the direction of motion:

• Example: A car speeding up on a straight highway.
  • In this case, the car is accelerating, and the acceleration is in the same direction as the motion (forward). This results in an increase in the car’s velocity.

• Example: A car coming to a stop at a traffic light.
  • Here, the car is decelerating, meaning the acceleration is acting opposite to the direction of motion. This causes the car to slow down until it comes to a complete stop.

• Example: A freely falling object (like a ball dropped from a height).
  • In this case, the object falls under the influence of gravity, and the acceleration due to gravity is constant (approximately $9.8 \, \text{m/s}^2$9.8m/s2) throughout the fall. This is an example of uniform acceleration.

• Example: A car driving through heavy traffic, where it speeds up and slows down irregularly.
  • In this scenario, the car’s velocity changes at varying rates over time, meaning the acceleration is not constant. This is an example of non-uniform acceleration.

Example 7.4 : Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 m s^–1 in 30 s. Then he applies brakes such that the velocity of the bicycle comes down to 4 m s^-1 in the next 5s. Calculate the acceleration of the bicycle in both the cases.

• Initial velocity (u): 0 m/s (Rahul starts from rest)
• Final velocity (v): 6 m/s
• Time taken (t): 30 s

• Initial velocity (u): 6 m/s
• Final velocity (v): 4 m/s
• Time taken (t): 5 s

7.4 - Graphical Representation of Motion

Graphs are an effective way to represent motion and show how different physical quantities change over time. In this section, we will explore how line graphs can describe motion, particularly using distance-time graphs.

7.4.1 - Distance-Time Graphs

• Definition: A graph that shows how an object's distance changes over time.
  • X-axis: Represents time.
  • Y-axis: Represents distance.
• Purpose: These graphs allow us to visualize how an object's position changes over time and help in understanding different types of motion (e.g., uniform speed, non-uniform speed).

1. Uniform Motion:
   • Definition: When an object moves with constant speed, covering equal distances in equal intervals of time.
   • Graph: The distance-time graph is a straight line, indicating that the distance increases uniformly with time.
     • Example: The portion OB in Fig. 7.3 represents uniform motion.
2. Non-Uniform Motion:
   • Definition: When an object moves with varying speed, covering unequal distances in equal intervals of time.
   • Graph: The distance-time graph for non-uniform motion is curved, indicating a varying rate of distance covered over time.
3. Rest:
   • Definition: When an object remains stationary.
   • Graph: The distance-time graph is a horizontal straight line, meaning that distance remains constant over time.

• Speed (v): The rate at which an object covers distance.
• To calculate speed from a distance-time graph, we use the formula: $$v=\frac{s_2-s_1}{t_2-t_1}$$
  • (s₂ – s₁): The change in distance (vertical distance or rise on the graph).
  • (t₂ – t₁): The change in time (horizontal distance or run on the graph).
• Example: In Fig. 7.3, point A and point B represent two points on the distance-time graph. The lines drawn from A to C (parallel to the x-axis) and from B to C (parallel to the y-axis) form a triangle. The speed can be determined by calculating the slope of this triangle (rise over run).

• Accelerated Motion: When the object's speed changes over time.
  • Graph: The distance-time graph for accelerated motion is curved, reflecting that the distance covered changes at varying rates.
  • Example: Table 7.2 provides data on a car's distance travelled in different time intervals, which can be plotted to observe how the distance changes over time, indicating acceleration.

• Uniform Speed: Constant speed; represented by a straight line on a distance-time graph.
• Non-uniform Speed: Changing speed; represented by a curved line on a distance-time graph.
• Rest: No motion; represented by a flat, horizontal line on a distance-time graph.
• Slope of Distance-Time Graph: Represents speed.
• Acceleration: Change in velocity over time; seen as a curve on a distance-time graph.

1. What does a straight line on a distance-time graph represent?
   • A straight line indicates uniform motion or constant speed.
2. How do you calculate speed from a distance-time graph?
   • Speed can be calculated by determining the slope of the graph, which is the change in distance divided by the change in time (rise over run).
3. What does a curved line on a distance-time graph signify?
   • A curved line indicates non-uniform motion or acceleration, where the object’s speed is changing over time.

Analysis of Table 7.2: Distance Travelled by a Car at Regular Time Intervals

The data in Table 7.2 shows how the distance travelled by a car increases over time. The values of time and corresponding distance are as follows:

1.3.3 - The Gaseous State

A velocity-time graph is a useful way to visualize how the velocity of an object changes with time when it is moving along a straight line. The x-axis represents time, while the y-axis represents velocity.

Uniform Velocity:

• Definition: When an object moves at constant velocity, its velocity remains unchanged over time.
• Graph: For uniform velocity, the velocity-time graph is a horizontal straight line parallel to the x-axis, indicating that velocity is constant at every instant of time.
  • Example: Fig. 7.5 shows the velocity-time graph for a car moving with a constant velocity of 40 km/h.

• The area under the velocity-time graph represents the displacement of the object.
• To find the displacement between time $t_1$ and $t_2$​:
  • Draw perpendicular lines from $t_1$ and $t_2$​ to the velocity line, forming a rectangle (as shown in Fig. 7.5).
  • The area of this rectangle gives the displacement, and it can be calculated using the formula: $$s=\text{velocity}\times \text{time}$$
  • For the car in Fig. 7.5, the displacement $s$s between $t_1$ and $t_2$​ is given by: $$s = \text{AC} \times \text{AB} = 40 \, \text{km/h} \times (t_2 - t_1) \, \text{hours}$$ This area gives the distance traveled in that time interval.

• Definition: When an object’s velocity changes by equal amounts in equal intervals of time, it is said to undergo uniformly accelerated motion.
• Graph: The velocity-time graph for uniformly accelerated motion is a straight line with a positive slope, indicating that the velocity is increasing at a constant rate.

• The velocity of a car is recorded at regular time intervals. The data is shown in Table 7.3:

• The velocity increases by a uniform amount (2.5 m/s) every 5 seconds. Therefore, the velocity-time graph (Fig. 7.6) is a straight line with a constant slope, indicating uniform acceleration.

• Uniform Velocity: The graph is a horizontal straight line, and the area under the line represents displacement.
• Uniformly Accelerated Motion: The graph is a straight line with a slope, indicating constant acceleration. The area under the graph gives the displacement, and the slope gives the acceleration.

Velocity-Time Graphs and Distance Calculations

1. Velocity-Time Graph and Distance:
   • The distance (or the magnitude of displacement) moved by a car can be determined by the area under the velocity-time graph.
   • The area represents the distance traveled over a given time interval.
   • If the car moves with uniform velocity, the distance is represented by a rectangle under the graph (refer to Fig. 7.6).
2. Non-Uniform Velocity:
   • When the car’s velocity is changing due to acceleration, the distance traveled will be the sum of two areas under the graph:
     • A rectangle representing the uniform velocity.
     • A triangle representing the change in velocity due to acceleration.
   • Formula for calculating the distance s:
     
     $$s = \text{Area ABCDE} = \text{Area of rectangle ABCD} + \text{Area of triangle ADE}$$
     $$s = AB \times BC + \frac{1}{2} \times AD \times DE$$
     • AB × BC: Represents the area of the rectangle (uniform velocity portion).
     • ½ (AD × DE): Represents the area of the triangle (acceleration portion).
3. Non-Uniformly Accelerated Motion:
   • For motion with non-uniform acceleration, velocity-time graphs can take various shapes.
   • Fig. 7.7(a): Represents the motion of an object with decreasing velocity over time.
   • Fig. 7.7(b): Shows non-uniform variation of velocity with time.
   • These graphs indicate complex motion patterns and need to be interpreted based on their shapes.
     
     

1. Train Motion Data (Table 7.4):
   • Stations A, B, and C with their distances from Station A and respective times of arrival and departure.

   Station	Distance from A (km)	Time of Arrival	Time of Departure
   A	0	08:00	08:15
   B	120	11:15	11:30
   C	180	13:00	13:15

2. Interpretation:
   • Between any two stations, assume uniform motion.
   • Plot the distance on the y-axis and time on the x-axis.
   • The slope of the graph between any two points represents the speed of the train between those stations.

1. Bicycle Motion Data (Table 7.5):
   • Distance covered by Feroz and Sania at different times.

   Time	Distance by Feroz (km)	Distance by Sania (km)
   8:00 am	0	0
   8:05 am	1.0	0.8
   8:10 am	1.9	1.6
   8:15 am	2.8	2.3
   8:20 am	3.6	3.0
   8:25 am	—	3.6

2. Plotting the Graph:
   • Both graphs should be plotted on the same scale with time on the x-axis and distance on the y-axis.
   • The slope of the lines represents the speed at different intervals.
   • Interpretation:
     • Feroz seems to move at a slightly faster rate compared to Sania, as he covers more distance in the same time.
     • Sania’s speed is slower but consistent.

1. Velocity-Time Graph: A graph that shows how velocity changes over time. The area under the graph represents the distance traveled.
2. Uniform Velocity: When an object travels at a constant speed, with no change in its velocity.
3. Acceleration: The rate of change of velocity over time.
4. Displacement: The shortest distance between the initial and final positions of an object.
5. Distance-Time Graph: A graph showing the distance covered by an object over time. The slope of the graph gives the speed.

7.5 - Equations of Motion

1. Equations of Motion:
   • These are a set of three equations that describe the relationship between velocity, acceleration, time, and distance when an object moves with uniform acceleration along a straight line.
   • These equations are useful to calculate the motion of objects without directly measuring all the variables.
2. Three Equations of Motion:
   • First Equation (Velocity-Time Relation): $$\begin{array}{cccc}& v=u+at& & \text{→ (7.5)}\end{array}$$
     • v: Final velocity of the object.
     • u: Initial velocity of the object.
     • a: Acceleration (rate of change of velocity).
     • t: Time for which the object moves.
     This equation gives the final velocity of an object after a certain time t, given its initial velocity u and the constant acceleration a. It describes how velocity changes over time.
   • Second Equation (Position-Time Relation): $$s = ut + \frac{1}{2} at^2 \tag{7.6}$$
     • s: Distance traveled by the object in time t.
     • u: Initial velocity of the object.
     • t: Time.
     • a: Acceleration.
     This equation calculates the distance covered by the object over a time period t, starting with initial velocity u and moving under constant acceleration a. It shows how position changes over time.
   • Third Equation (Position-Velocity Relation): $$2as = v^2 - u^2 \tag{7.7}$$
     • s: Distance traveled by the object.
     • a: Acceleration.
     • v: Final velocity.
     • u: Initial velocity.
     This equation links the distance traveled to the object’s initial and final velocities and acceleration, without involving time. It is useful when you need to find the distance covered but do not know the time.
3. Derivation:
   • These three equations can be derived using the graphical method from the velocity-time graph.
   • Eq. (7.7) is obtained by eliminating t from Eq. (7.5) and Eq. (7.6), combining them to relate position and velocity directly.

• Uniform Acceleration: Constant acceleration; the velocity of an object increases or decreases by the same amount in equal time intervals.
• Initial Velocity (u): The velocity of the object at the beginning of the time interval.
• Final Velocity (v): The velocity of the object at the end of the time interval.
• Distance (s): The total path covered by an object during the time interval.
• Time (t): The duration for which the object is in motion.
• Acceleration (a): The rate at which velocity changes with respect to time. It is constant for uniform acceleration.

Numerical Problems Based on Equations of Motion

Effect of Temperature on State of Matter

When the temperature of a solid is increased, the kinetic energy of its particles increases. As a result, the particles begin to vibrate more rapidly. When sufficient heat is supplied, the energy overcomes the forces of attraction between the particles, allowing them to break free from their fixed positions. At this stage, the solid begins to melt and converts into a liquid.

Melting Point:

• The melting point of a solid is the minimum temperature at which it changes into a liquid under atmospheric pressure. It indicates the strength of the forces of attraction between the particles of the solid.
• Melting point of ice: 273.15 K (0°C).

• The process of melting, where a solid changes into a liquid, is called fusion.

• The word latent means "hidden."
• The latent heat of fusion is the amount of heat energy required to change 1 kg of a solid into a liquid at atmospheric pressure at its melting point.

• Boiling point of water: 373 K (100°C).
• Boiling is a bulk phenomenon where particles from the entire bulk of the liquid gain energy and change into vapor.

• Steam at 373 K contains more energy than water at the same temperature due to the absorption of latent heat.

1. Latent Heat of Fusion: The amount of heat energy required to convert 1 kg of a solid into liquid at atmospheric pressure at its melting point.
2. Latent Heat of Vaporization: The amount of heat energy required to convert 1 kg of a liquid into gas at atmospheric pressure at its boiling point.

7.6 - Uniform Circular Motion

Definition:

• Uniform Circular Motion: It is the motion of an object moving at a constant speed along a circular path. The object's velocity changes due to a continuous change in direction, even though its speed remains constant.

1. Acceleration:
   • An object is said to be accelerating if there is a change in its velocity, which can be due to a change in magnitude (speed) or direction. In uniform circular motion, the speed remains constant, but the direction changes continuously.
2. Direction Changes in Closed Paths:
   • When an athlete runs around a closed path, they must change direction at each corner:
     • Rectangular Track (ABCD): 4 direction changes.
     • Hexagonal Track (ABCDEF): 6 direction changes.
     • Octagonal Track (ABCDEFGH): 8 direction changes.
3. As the number of sides increases:
   • The shape of the track approaches that of a circle. Consequently, the length of each side decreases, and the need for direction changes increases.
4. Motion Along a Circular Path:
   • If the athlete runs along a circular path with a constant speed, the only change in velocity is due to the change in direction of motion, which constitutes accelerated motion.
5. Circumference and Speed:
   • The circumference $C$ of a circle is given by the formula: $$C = 2\pi r$$ Where $r$ is the radius.
   • If the time taken to complete one round is $t$, the speed $v$ is calculated as: $$v=\frac{2\pi r}{\mathrm{t\; <span\; style="font-size:\; 1.07rem;"></span>}}$$

• Activity 7.11:
  • Materials Needed: A piece of thread and a small stone.
  • Procedure:
    1. Tie a small stone to one end of the thread and swing it to describe a circular path at constant speed.
    2. Release the stone at various points along the circular path.
  • Observation: Upon release, the stone moves in a straight line tangential to the circular path at the point of release.

• When an object in circular motion is released, it moves straight in the direction it was heading at the moment of release, illustrating the principle that an object in motion tends to stay in motion in a straight line unless acted upon by an external force.

• The motion of planets (e.g., the Earth around the Sun).
• Satellites in orbit around the Earth.
• Cyclists maintaining a constant speed on a circular track.
• Athletes throwing hammers or discs.

1. What happens when the stone is released?
   • Upon release, the stone moves in a straight line that is tangent to the circular path at the point of release. This demonstrates the tendency of objects in motion to continue in their current direction unless acted upon by an external force.
2. Does the direction of motion change while the stone is moving in a circular path?
   • Yes, the direction of motion changes continuously as the stone moves along the circular path.
3. Why is uniform circular motion considered accelerated motion?
   • Even though the speed is constant, the velocity is changing due to the continuous change in direction, making it a form of accelerated motion.

NCERT Science Notes - Class 9 | Science | Chapter 7 - Motion

NCERT Science Notes - Class 9 | Science | Chapter 7 - Motion