Class 9 Science NCERT Notes – Chapter 7: Motion (PDF, MindMap, Q&A, Quizzes)

Chapter 7 (Physics): Motion – Class 9 NCERT Science Detailed Study Notes.

1. The Concept of Motion

Motion is a fundamental phenomenon observed everywhere, from atoms and molecules to planets and galaxies. An object is perceived to be in motion when its position changes with time.

• Relativity of Motion: Motion is relative to the observer’s frame of reference. An object can appear to be moving to one person and stationary to another. For example, to passengers on a moving bus, roadside trees seem to move backward, while a person on the roadside sees the bus and its passengers as moving. A passenger inside the bus sees fellow passengers at rest.
• Reference Point: To describe the position of an object, a specific reference point, called the origin, must be specified. For instance, stating a school is “2 km north of the railway station” uses the railway station as the reference point.
• Types of Motion: Motions can be complex and varied. This guide focuses on motion along a straight line (linear motion) and circular motion. Other types include rotational and vibratory motion.

2. Motion Along a Straight Line

The simplest type of motion is movement along a straight path.

2.1 Distance and Displacement

Two physical quantities are used to describe the overall motion and final position of an object:

• Distance: The total path length covered by an object. It is a scalar quantity, meaning it is described only by its numerical value (magnitude) and does not require a direction.
  • Example: If an object travels from a starting point O to point A (60 km away) and then returns to point C (25 km from O), the total distance covered is 60 km + (60 km – 25 km) = 95 km.
• Displacement: The shortest distance measured from the initial position to the final position of an object. It is a vector quantity, requiring both magnitude and direction, although this guide focuses on its magnitude.
  • Example: In the same scenario, the displacement is the distance from the initial point O to the final point C, which is 25 km.

Key Differences between Distance and Displacement:

Feature	Distance	Displacement
Definition	Total path length covered.	Shortest distance between initial and final points.
Magnitude	Always positive and non-zero if the object has moved.	Can be positive, negative, or zero.
Comparison	The magnitude of distance is always greater than or equal to the magnitude of displacement.	The magnitude of displacement can be zero even if the distance is not (e.g., a round trip).

An object can have zero displacement if it returns to its initial starting position, even though it has covered a non-zero distance.

3. Types of Linear Motion

3.1 Uniform Motion

An object is in uniform motion when it covers equal distances in equal intervals of time. In day-to-day life, perfectly uniform motion is rare.

• Graphical Representation: The distance-time graph for uniform motion is a straight line.

3.2 Non-Uniform Motion

An object is in non-uniform motion when it covers unequal distances in equal intervals of time. Most real-world motions, such as a car in traffic or a person jogging, are non-uniform.

• Graphical Representation: The distance-time graph for non-uniform motion is a curved line.

4. Measuring the Rate of Motion

4.1 Speed

Speed is the rate of motion, defined as the distance travelled by an object in unit time.

• Nature: It is a scalar quantity, requiring only magnitude.
• Formula: v = s / t, where v is speed, s is distance, and t is time.
• SI Unit: metre per second (m/s or m s⁻¹). Other common units include kilometre per hour (km/h) and centimetre per second (cm/s).
• Average Speed: For non-uniform motion, the rate is described by average speed, calculated by dividing the total distance travelled by the total time taken.
  • Formula: Average Speed = Total distance travelled / Total time taken

4.2 Velocity

Velocity provides a more comprehensive measure of motion by specifying both speed and direction.

• Nature: It is the speed of an object moving in a definite direction. Velocity can change by altering the object’s speed, its direction of motion, or both.
• SI Unit: Same as speed, m/s or m s⁻¹.
• Average Velocity:
  1. Calculated similarly to average speed: Average Velocity = Displacement / Total time taken.
  2. For an object with velocity changing at a uniform rate, it is the arithmetic mean of the initial and final velocities:
     • Formula: v_av = (u + v) / 2, where u is the initial velocity and v is the final velocity.

The magnitude of average velocity is equal to the average speed only when an object moves along a straight line in the same direction.

5. Rate of Change of Velocity: Acceleration

Acceleration is the measure of the change in the velocity of an object per unit of time. An object’s motion is considered accelerated if its velocity changes.

• Formula: a = (v - u) / t, where a is acceleration, v is final velocity, u is initial velocity, and t is the time taken.
• SI Unit: metre per second squared (m/s² or m s⁻²).
• Direction:
  • Positive Acceleration: Occurs when the acceleration is in the direction of the velocity (speeding up).
  • Negative Acceleration (Deceleration/Retardation): Occurs when acceleration is opposite to the direction of velocity (slowing down).
• Types of Acceleration:
  • Uniform Acceleration: An object has uniform acceleration if it travels in a straight line and its velocity changes by equal amounts in equal intervals of time. A freely falling body is a classic example.
  • Non-Uniform Acceleration: An object has non-uniform acceleration if its velocity changes at a non-uniform rate. For example, a car’s speed increasing by unequal amounts in equal time intervals.

6. Graphical Representation of Motion

Graphs are a convenient tool for representing and analyzing motion.

6.1 Distance-Time Graphs

• Axes: Time is plotted on the x-axis, and distance is on the y-axis.
• Interpretations:
  • Uniform Speed/Velocity: A straight line graph. The slope of the line gives the speed: v = (s₂ – s₁) / (t₂ – t₁).
  • Non-Uniform Speed: A curved line graph.
  • Object at Rest: A straight line parallel to the time axis (x-axis).

6.2 Velocity-Time Graphs

• Axes: Time is plotted on the x-axis, and velocity is on the y-axis.
• Interpretations:
  • Uniform Velocity: A straight line parallel to the time axis. The area under the graph represents the magnitude of the displacement (distance = velocity × time).
  • Uniformly Accelerated Motion: A straight, sloped line. The slope of the graph gives the acceleration. The area under the graph gives the distance travelled.
  • Non-Uniformly Accelerated Motion: The graph can be any shape (e.g., a curve).

7. Equations of Motion for Uniformly Accelerated Motion

For an object moving along a straight line with uniform acceleration (a), its motion can be described by a set of three equations:

1. Velocity-Time Relation: v = u + at
2. Position-Time Relation: s = ut + ½ at²
3. Position-Velocity Relation: 2as = v² – u²

Where:

• u = initial velocity
• v = final velocity
• a = uniform acceleration
• t = time
• s = distance travelled

8. Uniform Circular Motion

This is the motion of an object moving in a circular path with uniform speed.

• Accelerated Motion: Although the speed is constant, the direction of motion changes continuously at every point. Since velocity depends on direction, the velocity is constantly changing, which means the motion is accelerated.
• Direction of Velocity: At any point on the circular path, the direction of motion is tangential to the path at that point. If an object is released, it will travel along this tangent.
• Speed Calculation: The speed (v) of an object in uniform circular motion is given by:
  • Formula: v = 2πr / t, where r is the radius of the circular path and t is the time taken to complete one revolution.
• Examples: Motion of the moon around the Earth, a satellite in a circular orbit, an athlete on a circular track.

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Q&A Section

Part A: Short-Answer Questions

Answer each question in 2-3 sentences.

1. Why is motion considered a relative concept?
2. What is a reference point, and why is it essential for describing an object’s position?
3. Define distance and explain what kind of physical quantity it is.
4. Define displacement and explain how it differs from distance.
5. Is it possible for an object to have moved a certain distance but have a displacement of zero? Provide an example.
6. What are the characteristics of an object in uniform motion?
7. Describe non-uniform motion with a real-world example.
8. How is the average speed of an object calculated, and why is this measure useful?
9. What is velocity, and how can an object’s velocity be changed?
10. Under what specific condition is the magnitude of an object’s average velocity equal to its average speed?
11. What physical quantity is measured by an automobile’s odometer?
12. Define acceleration and state its SI unit.
13. What is the difference between positive and negative acceleration?
14. Explain what is meant by uniform acceleration and provide an example.
15. What does the slope of a distance-time graph represent?
16. What does a straight line parallel to the time axis on a distance-time graph indicate about an object’s motion?
17. How can the distance travelled by an object be determined from its velocity-time graph?
18. What does the slope of a velocity-time graph represent?
19. Name the three equations of motion for an object moving with uniform acceleration.
20. Why is uniform circular motion considered an example of accelerated motion, even if the speed is constant?
21. If a stone being whirled in a circle is released, in what direction will it travel?
22. What does a curved line on a distance-time graph signify?
23. How is the average velocity calculated for an object whose velocity is changing at a uniform rate?
24. List two examples of uniform circular motion from everyday life.
25. How does the shape of an athlete’s path change as the number of sides on a track increases indefinitely?

Part B: Multiple-Choice Questions

Select the best answer for each question.

1. To describe the position of an object, we need to specify a reference point called the…
   • a) Magnitude b) Origin c) Axis d) Velocity
2. The numerical value of a physical quantity is its…
   • a) Displacement b) Velocity c) Magnitude d) Acceleration
3. The shortest distance measured from the initial to the final position of an object is known as…
   • a) Distance b) Speed c) Path length d) Displacement
4. Which of the following is true for displacement?
   • a) It cannot be zero. b) It is always equal to the distance. c) Its magnitude can be zero even if the distance is not. d) Its magnitude is always greater than the distance.
5. An object that covers equal distances in equal intervals of time is said to be in…
   • a) Non-uniform motion b) Uniform motion c) Accelerated motion d) Circular motion
6. The SI unit of speed is…
   • a) km/h b) cm/s c) m/s² d) m/s
7. Velocity is defined as…
   • a) Distance per unit time b) Displacement per unit time c) The rate of change of position d) The total path length covered
8. The SI unit of acceleration is…
   • a) m s⁻¹ b) km h⁻¹ c) m s⁻² d) m/km
9. A freely falling body is an example of…
   • a) Non-uniformly accelerated motion b) Uniform velocity c) Uniformly accelerated motion d) Uniform circular motion
10. On a distance-time graph, a straight line indicates…
    • a) The object is at rest b) The object is in non-uniform motion c) The object is in uniform motion d) The object is accelerating uniformly
11. The area under a velocity-time graph represents the…
    • a) Acceleration b) Average speed c) Change in velocity d) Magnitude of the displacement
12. If a car’s velocity-time graph is a straight line parallel to the time axis, the car is…
    • a) Accelerating b) At rest c) Moving with uniform velocity d) In non-uniform motion
13. The equation that represents the position-time relation for uniform acceleration is…
    • a) v = u + at b) 2as = v² – u² c) s = ut + ½ at² d) v = s / t
14. Negative acceleration means that the acceleration is…
    • a) In the same direction as velocity b) Perpendicular to the direction of velocity c) Equal to zero d) Opposite to the direction of velocity
15. An athlete running on a hexagonal track has to change direction…
    • a) Four times b) Six times c) Eight times d) Indefinitely
16. In uniform circular motion…
    • a) Both speed and velocity are constant b) Speed is constant, but velocity is changing c) Velocity is constant, but speed is changing d) Both speed and velocity are changing
17. A device used in automobiles to show the distance travelled is the…
    • a) Speedometer b) Manometer c) Odometer d) Barometer
18. An object travels 16 m in 4 s and then another 16 m in 2 s. What is the average speed?
    • a) 5.33 m/s b) 8 m/s c) 4 m/s d) 6 m/s
19. The equation of motion v = u + at describes the…
    • a) Position-time relation b) Position-velocity relation c) Velocity-displacement relation d) Velocity-time relation
20. When a stone on a thread is whirled in a circle, the velocity at any point is directed…
    • a) Towards the center of the circle b) Away from the center of the circle c) Tangential to the circular path d) Opposite to the direction of motion

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Answer Keys

Answer Key: Part A (Short-Answer Questions)

1. Motion is relative because an object’s movement is perceived differently depending on the observer’s own state of motion. For example, passengers on a train see each other at rest, but an observer on the platform sees them moving.
2. A reference point, or origin, is a fixed point from which an object’s location is described. It is essential because without it, there is no way to specify the position of an object.
3. Distance is the total path length covered by a moving object. It is a scalar quantity, which means it is described only by its numerical value, or magnitude, without a specified direction.
4. Displacement is the shortest distance between an object’s initial and final positions. Unlike distance, its magnitude can be zero, and it is fundamentally a vector quantity (though the text focuses on magnitude).
5. Yes, an object can have zero displacement after covering a non-zero distance. This occurs when the object’s final position is the same as its initial position, such as completing a full lap on a circular track or returning home after a trip.
6. An object in uniform motion travels equal distances in equal intervals of time. Its path, when moving along a straight line, is represented by a straight line on a distance-time graph.
7. Non-uniform motion occurs when an object covers unequal distances in equal intervals of time. A common example is a car moving on a crowded street, where its speed constantly changes.
8. Average speed is calculated by dividing the total distance travelled by the total time taken. It is useful for describing the overall rate of motion for an object that is not moving at a constant speed.
9. Velocity is the speed of an object moving in a definite direction. An object’s velocity can be changed by changing its speed, its direction of motion, or both.
10. The magnitude of an object’s average velocity is equal to its average speed only when the object travels along a straight line in the same direction without changing direction.
11. An automobile’s odometer measures the total distance travelled by the vehicle.
12. Acceleration is the rate of change of velocity of an object per unit time. Its SI unit is metres per second squared (m/s²).
13. Positive acceleration occurs when the acceleration is in the same direction as the object’s velocity, causing it to speed up. Negative acceleration (deceleration) is when the acceleration is in the opposite direction of the velocity, causing the object to slow down.
14. Uniform acceleration means that an object’s velocity changes by equal amounts in equal intervals of time while it moves in a straight line. The motion of a freely falling body is an example of this.
15. The slope of a distance-time graph represents the speed (or velocity) of the object. A steeper slope indicates a higher speed.
16. A straight line parallel to the time axis on a distance-time graph indicates that the object’s position is not changing over time. Therefore, the object is at rest.
17. The distance travelled by an object can be determined from its velocity-time graph by calculating the area enclosed between the graph line and the time axis for the given time interval.
18. The slope of a velocity-time graph represents the acceleration of the object. A positive slope indicates acceleration, a negative slope indicates deceleration, and a zero slope indicates constant velocity.
19. The three equations of motion are: v = u + at (velocity-time), s = ut + ½ at² (position-time), and 2as = v² – u² (position-velocity).
20. Uniform circular motion is an accelerated motion because the direction of the velocity is constantly changing as the object moves along the circular path. A change in velocity, whether in magnitude or direction, constitutes acceleration.
21. If a stone being whirled in a circle is released, it will continue to move along a straight line that is tangential to the circular path at the point of release.
22. A curved line on a distance-time graph signifies that the object is covering unequal distances in equal time intervals. This represents non-uniform speed or accelerated motion.
23. For an object with velocity changing at a uniform rate, the average velocity is the arithmetic mean of the initial velocity (u) and final velocity (v), given by the formula v_av = (u + v) / 2.
24. Two examples of uniform circular motion are the motion of the moon around the Earth and an artificial satellite moving in a circular orbit around the Earth.
25. As the number of sides on an athlete’s track increases indefinitely, the shape of the track approaches the shape of a circle, and the length of each side decreases to a point.

Answer Key: Part B (Multiple-Choice Questions)

1. b) Origin
2. c) Magnitude
3. d) Displacement
4. c) Its magnitude can be zero even if the distance is not.
5. b) Uniform motion
6. d) m/s
7. b) Displacement per unit time (Note: The text also defines it as speed in a definite direction, but this is the formal calculation).
8. c) m s⁻²
9. c) Uniformly accelerated motion
10. c) The object is in uniform motion
11. d) Magnitude of the displacement
12. c) Moving with uniform velocity
13. c) s = ut + ½ at²
14. d) Opposite to the direction of velocity
15. b) Six times
16. b) Speed is constant, but velocity is changing
17. c) Odometer
18. a) 5.33 m/s (Total distance = 32 m, Total time = 6 s. Average speed = 32/6 = 5.33 m/s)
19. d) Velocity-time relation
20. c) Tangential to the circular path

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Essay Questions and Answers

1. Distinguish clearly between distance and displacement. Use the numerical example of motion along a straight line path from O to A and back to C (as described in the text) to illustrate the differences in calculation and meaning.

Answer: Distance and displacement are two fundamental quantities used to describe motion, but they have distinct meanings. Distance is the total path length an object covers during its motion. It is a scalar quantity, meaning it is defined solely by its magnitude. In contrast, displacement is the shortest distance between an object’s initial and final positions, effectively a straight line from start to finish. It is a vector quantity, possessing both magnitude and direction.

The example from the text illustrates this difference perfectly. An object starts at a reference point O, travels to point A located 60 km away, and then moves back along the same path to point C, which is 25 km from O.

• To calculate the distance: We must sum the entire path travelled. The journey from O to A is 60 km. The return journey from A to C is the difference between their positions from O, which is 60 km – 25 km = 35 km. Therefore, the total distance covered is 60 km + 35 km = 95 km.
• To calculate the displacement: We only consider the initial and final positions. The object started at O (0 km) and ended at C (25 km). The displacement is the direct distance from O to C, which is simply 25 km. This shows that while the object travelled a total of 95 km, its final position is only 25 km from where it started.

2. Explain the concepts of uniform and non-uniform motion. How are these two types of motion represented on a distance-time graph?

Answer: Uniform and non-uniform motion describe how an object’s speed varies over time.

• Uniform Motion: An object is in uniform motion if it covers equal distances in equal intervals of time, no matter how small the time intervals are. This implies that the object is moving at a constant speed in a constant direction (i.e., constant velocity).
• Non-Uniform Motion: An object is in non-uniform motion if it covers unequal distances in equal intervals of time. This is the case for most real-world scenarios, such as a car accelerating, decelerating, or moving through traffic. This implies its speed or velocity is changing.

These two types of motion are represented distinctly on a distance-time graph, where time is on the x-axis and distance is on the y-axis:

• Graph for Uniform Motion: Because the distance travelled is directly proportional to the time taken, the graph for uniform motion is a straight line. The constant slope of this line represents the constant speed of the object.
• Graph for Non-Uniform Motion: The graph for non-uniform motion is a curved line. The non-linear nature of the graph shows that the distance travelled is not changing at a constant rate with respect to time, indicating a variable speed.

3. Define speed and velocity, highlighting the key distinction between them. Using the example of Usha swimming in a pool, explain how an object can have a non-zero average speed but a zero average velocity.

Answer: Speed and velocity both measure the rate of motion, but velocity includes directional information.

• Speed: Speed is the distance an object travels per unit of time. It is a scalar quantity, described only by its magnitude (e.g., 50 km/h).
• Velocity: Velocity is the speed of an object moving in a definite direction. It can also be defined as the displacement per unit of time. It is a vector quantity. An object’s velocity changes if its speed changes, its direction changes, or both.

The key distinction is direction. Two objects can have the same speed but different velocities if they are moving in different directions.

The example of Usha swimming in a 90 m long pool perfectly illustrates this. She swims 180 m in one minute by going from one end to the other and back again.

• Average Speed Calculation: Her total distance covered is 180 m, and the total time taken is 1 minute (60 s). Her average speed is Total Distance / Total Time = 180 m / 60 s = 3 m/s. This is a non-zero value representing the rate at which she covered the path.
• Average Velocity Calculation: Her displacement is the shortest distance between her initial and final positions. Since she starts at one end and returns to the same end, her final position is the same as her initial position. Therefore, her displacement is 0 m. Her average velocity is Displacement / Total Time = 0 m / 60 s = 0 m/s. This shows that despite moving, her net change in position over that minute was zero.

4. What is acceleration? Explain the difference between uniform and non-uniform acceleration and provide a real-world example for each.

Answer: Acceleration is the physical quantity that measures the rate of change of an object’s velocity over time. An object is accelerating whenever its velocity is changing, which can be a change in speed, direction, or both. The formula for acceleration is a = (v - u) / t, and its SI unit is m/s².

The primary difference between uniform and non-uniform acceleration lies in the rate at which the velocity changes.

• Uniform Acceleration: An object experiences uniform acceleration when its velocity changes by equal amounts in equal intervals of time, assuming it is moving in a straight line. The acceleration value remains constant throughout the motion. A classic real-world example is the motion of a freely falling body. Under the influence of gravity (and neglecting air resistance), its velocity increases at a constant rate (approximately 9.8 m/s every second).
• Non-Uniform Acceleration: An object experiences non-uniform acceleration when its velocity changes at a non-uniform rate. The change in velocity is different in equal intervals of time. An example is a car travelling along a straight road in traffic. Its speed increases and decreases by unequal amounts in equal time intervals as it navigates around other vehicles, meaning its acceleration is constantly changing.

5. Describe how a velocity-time graph can be used to determine both the acceleration of an object and the distance it travels. Use the case of uniform acceleration as your primary example.

Answer: A velocity-time graph, which plots time on the x-axis and velocity on the y-axis, is a powerful tool for analyzing motion.

1. Determining Acceleration: The acceleration of an object is represented by the slope (or gradient) of its velocity-time graph. For uniformly accelerated motion, the graph is a straight, sloped line. The constant slope indicates constant acceleration. A positive slope means positive acceleration (speeding up), while a negative slope means negative acceleration (slowing down). A zero slope (a horizontal line) indicates zero acceleration, meaning constant velocity.
2. Determining Distance: The distance travelled by an object (or the magnitude of its displacement) is represented by the area under the velocity-time graph for a given time interval. For an object moving with uniform acceleration starting from an initial velocity, the area under the graph is often a trapezoid. This area can be calculated by dividing it into a rectangle and a triangle. The area of the rectangle (length × width) corresponds to the distance that would be covered if the object maintained its initial velocity, and the area of the triangle (½ × base × height) corresponds to the additional distance covered due to acceleration. The total distance s is the sum of these two areas.

For example, if a car accelerates uniformly, the distance travelled is the area of the shape ABCDE as shown in Fig. 7.6 of the source text, calculated as s = area of rectangle ABCD + area of triangle ADE.

6. What is uniform circular motion? Explain why it is considered an accelerated motion and describe how to calculate the speed of an object undergoing it.

Answer: Uniform circular motion is the motion of an object travelling at a constant (uniform) speed along a circular path. Examples include a satellite orbiting the Earth at a constant altitude or a cyclist riding on a circular track at a steady pace.

Although the object’s speed remains constant, this type of motion is considered accelerated motion. The reason lies in the definition of velocity. Velocity is a vector quantity that includes both magnitude (speed) and direction. In circular motion, the object’s direction of movement is continuously changing at every point along the path. At any instant, the velocity is tangential to the circle. Since the direction of velocity is changing, the velocity itself is changing, and any change in velocity over time is, by definition, acceleration.

The speed (v) of an object in uniform circular motion can be calculated using the distance it travels in one full revolution (the circumference of the circle) and the time it takes to complete that revolution (t). The circumference of a circle with radius r is 2πr. Therefore, the formula for speed is: v = 2πr / t

7. List and define the variables in the three standard equations of motion. Provide a brief explanation of what each equation relates.

Answer: The three standard equations of motion describe the relationship between displacement, velocity, acceleration, and time for an object moving in a straight line with uniform acceleration. The variables are:

• u: The initial velocity of the object.
• v: The final velocity of the object after time t.
• a: The uniform acceleration of the object.
• s: The distance (or displacement) travelled by the object in time t.
• t: The time interval during which the motion occurs.

The three equations and their relationships are:

1. v = u + at: This is the velocity-time relation. It relates the final velocity to the initial velocity, acceleration, and the time elapsed. It essentially defines acceleration in a rearranged form.
2. s = ut + ½ at²: This is the position-time relation. It calculates the distance travelled based on the initial velocity, acceleration, and the time interval. It is used to find the position of an object at any given time.
3. 2as = v² – u²: This is the position-velocity relation. It relates the final velocity, initial velocity, acceleration, and distance, notably without requiring the time interval t. It is useful for finding the final velocity after an object has travelled a certain distance or vice-versa.

8. Imagine a bus that starts from rest and moves with a uniform acceleration of 0.1 m/s² for 2 minutes. Explain, step-by-step, how you would use the equations of motion to find (a) the speed it acquires and (b) the distance it travels.

Answer: To solve this problem, we first identify the known variables from the problem statement and convert them to standard SI units.

• Initial velocity (u) = 0 m/s (since the bus starts from rest).
• Uniform acceleration (a) = 0.1 m/s².
• Time (t) = 2 minutes. We must convert this to seconds: 2 min × 60 s/min = 120 s.

(a) Finding the final speed acquired (v): To find the final speed, we need an equation that relates v, u, a, and t. The first equation of motion, v = u + at, is perfect for this.

• Step 1: Write down the equation: v = u + at.
• Step 2: Substitute the known values: v = 0 + (0.1 m/s²) × (120 s).
• Step 3: Calculate the result: v = 12 m/s. So, the speed acquired by the bus after 2 minutes is 12 m/s.

(b) Finding the distance travelled (s): To find the distance, we can use the second equation of motion, s = ut + ½ at², as we know u, a, and t.

• Step 1: Write down the equation: s = ut + ½ at².
• Step 2: Substitute the known values: s = (0 m/s × 120 s) + ½ × (0.1 m/s²) × (120 s)².
• Step 3: Calculate the result: s = 0 + 0.5 × 0.1 × 14400 m = 0.05 × 14400 m = 720 m. Alternatively, we could use the third equation, 2as = v² – u², now that we know v.
• Step 1: Rearrange to solve for s: s = (v² – u²) / 2a.
• Step 2: Substitute values: s = ((12 m/s)² – (0 m/s)²) / (2 × 0.1 m/s²).
• Step 3: Calculate: s = 144 / 0.2 m = 720 m. Both methods show that the distance travelled by the bus is 720 meters.

9. Discuss the importance of graphical representation in studying motion. What key information can be derived from the shape and slope of distance-time and velocity-time graphs?

Answer: Graphical representation is a crucial tool in studying motion because it provides a convenient and intuitive visual method to present complex information about an object’s movement over time. Graphs allow for the immediate interpretation of the nature of motion—whether it is uniform, non-uniform, at rest, or accelerating—and enable quantitative analysis without complex calculations.

From a Distance-Time Graph:

• Shape: The shape of the graph reveals the type of motion. A straight line parallel to the time axis means the object is at rest. A straight, sloped line indicates uniform motion (constant speed). A curved line indicates non-uniform motion (changing speed).
• Slope: The slope (gradient) of the distance-time graph represents the speed of the object. A steeper slope signifies a higher speed, while a gentler slope signifies a lower speed.

From a Velocity-Time Graph:

• Shape: A straight line parallel to the time axis represents uniform velocity (zero acceleration). A straight, sloped line indicates uniformly accelerated motion. A curved line represents non-uniformly accelerated motion.
• Slope: The slope of the velocity-time graph represents the acceleration of the object. A positive slope indicates positive acceleration, a negative slope indicates negative acceleration (deceleration), and a zero slope indicates zero acceleration.
• Area Under the Graph: The area enclosed by the velocity-time graph and the time axis gives the magnitude of the displacement (or distance travelled) of the object during that time interval. This feature allows for the calculation of distance even when the motion is complex.

10. An athlete runs on a rectangular track, then a hexagonal track, and finally a circular track. Describe how the concept of acceleration applies to the athlete’s motion on each track, assuming they maintain a constant speed.

Answer: This scenario illustrates how acceleration is intrinsically linked to a change in velocity, which includes a change in direction.

• Rectangular Track: On a rectangular track, the athlete runs at a constant speed along four straight segments (AB, BC, CD, DA). Along each straight part, the velocity is constant, and there is zero acceleration. However, at each of the four corners, the athlete must quickly change direction to stay on the track. This change in direction constitutes a change in velocity, meaning the athlete accelerates at each of the four corners.
• Hexagonal Track: A hexagonal track has six straight segments and six corners. Similar to the rectangular track, the athlete moves with constant velocity along the straight parts but must accelerate at each of the six corners to change direction. The athlete has to change direction more frequently than on the rectangular track.
• Circular Track: As the number of sides of the track increases, the path begins to resemble a circle. On a perfectly circular track, there are no straight segments or distinct corners. The athlete’s direction of motion is changing continuously at every single point along the path. Even if the athlete maintains a constant speed, this continuous change in direction means their velocity is constantly changing. Therefore, the athlete is undergoing continuous acceleration throughout their entire motion on the circular track. This specific type of motion is known as uniform circular motion, which is a form of accelerated motion.

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Glossary of Key Terms

• Acceleration: The rate of change of the velocity of an object per unit time. Its SI unit is m/s².
• Average Speed: The total distance travelled by an object divided by the total time taken.
• Average Velocity: The displacement of an object divided by the total time taken; for uniformly changing velocity, it is the arithmetic mean of the initial and final velocities.
• Distance: The total path length covered by an object during its motion.
• Distance-Time Graph: A line graph that represents the change in the position of an object with time, with time on the x-axis and distance on the y-axis.
• Displacement: The shortest distance measured from the initial to the final position of an object.
• Magnitude: The numerical value of a physical quantity.
• Motion: The phenomenon in which an object changes its position over time.
• Non-Uniform Acceleration: A type of motion where an object’s velocity changes at a non-uniform rate.
• Non-Uniform Motion: A type of motion in which an object covers unequal distances in equal intervals of time.
• Odometer: A device in automobiles that measures and displays the total distance travelled.
• Origin: A fixed reference point used to describe the location of an object.
• Reference Point: A point used to specify the position of an object.
• Speed: The distance travelled by an object in unit time. Its SI unit is m/s.
• Uniform Acceleration: A type of motion where an object travelling in a straight line increases or decreases its velocity by equal amounts in equal intervals of time.
• Uniform Circular Motion: The motion of an object moving in a circular path with uniform speed.
• Uniform Motion: A type of motion in which an object covers equal distances in equal intervals of time.
• Velocity: The speed of an object moving in a definite direction. Its SI unit is m/s.
• Velocity-Time Graph: A graph showing the variation in velocity with time, with time on the x-axis and velocity on the y-axis.