Class 9 Science Notes Chapter 8 (Chapter 8) – Examplar Problem (English) Book

Alright class, let's focus on Chapter 8, 'Motion', from the NCERT Class 9 Science framework. This chapter is fundamental for understanding mechanics and frequently appears in various government examinations. We will cover the key concepts precisely.

Chapter 8: Motion - Detailed Notes for Exam Preparation

1. Motion and Rest:

• Rest: An object is said to be at rest if its position does not change with respect to a fixed point (reference point or origin) in its surroundings.
• Motion: An object is said to be in motion if its position changes continuously with respect to a reference point.
• Reference Point (Origin): A fixed point or object with respect to which the position of another object is described. Motion is relative; an object can be in motion relative to one reference point and at rest relative to another.
• Example: A passenger inside a moving bus is at rest with respect to fellow passengers but in motion with respect to a tree outside.

2. Types of Motion:

• Linear Motion (or Rectilinear Motion): Motion along a straight line.
• Circular Motion: Motion along a circular path.
• Oscillatory Motion: To and fro motion about a mean position.

3. Scalar and Vector Quantities:

• Scalar Quantity: A physical quantity that has only magnitude but no direction. Examples: Distance, Speed, Mass, Time, Temperature, Work, Energy.
• Vector Quantity: A physical quantity that has both magnitude and direction. Examples: Displacement, Velocity, Acceleration, Force, Momentum.

4. Distance and Displacement:

• Distance:
  • The actual length of the path covered by a moving object, irrespective of the direction.
  • It is a scalar quantity.
  • It can never be zero or negative for a moving object.
  • SI unit: metre (m).
• Displacement:
  • The shortest distance between the initial and final positions of a moving object, measured in a specific direction.
  • It is a vector quantity.
  • It can be positive, negative, or zero. (Zero displacement occurs when the final position coincides with the initial position, e.g., one complete circle).
  • Magnitude of displacement is always less than or equal to the distance travelled. (|Displacement| ≤ Distance).
  • SI unit: metre (m).

5. Uniform and Non-uniform Motion:

• Uniform Motion: An object is said to be in uniform motion if it travels equal distances in equal intervals of time, however small the intervals may be. This implies constant speed and, if moving in a straight line, constant velocity. The path is typically a straight line.
• Non-uniform Motion: An object is said to be in non-uniform motion if it travels unequal distances in equal intervals of time. This implies variable speed or variable velocity. Most real-life motions are non-uniform.

6. Speed:

• The rate at which an object covers distance.
• Speed = Distance / Time
• It is a scalar quantity.
• SI unit: metre per second (m/s or ms⁻¹). Other units: km/h, cm/s.
• Average Speed: For non-uniform motion, it is the ratio of the total distance travelled to the total time taken.
  • Average Speed = Total Distance / Total Time Taken

7. Velocity:

• The rate at which an object changes its position; it is the speed of an object in a specific direction.
• Velocity = Displacement / Time
• It is a vector quantity.
• SI unit: metre per second (m/s or ms⁻¹).
• Velocity can be changed by changing speed, direction, or both.
• Uniform Velocity: An object moving with uniform velocity covers equal displacements in equal intervals of time. It implies motion along a straight line with constant speed.
• Average Velocity: For an object moving with variable velocity, it is the ratio of the total displacement to the total time taken.
  • Average Velocity = Total Displacement / Total Time Taken
  • For uniformly changing velocity (uniform acceleration), Average Velocity = (Initial Velocity + Final Velocity) / 2 = (u + v) / 2

8. Acceleration:

• The rate of change of velocity of an object with time.
• Acceleration (a) = Change in Velocity / Time Taken = (Final Velocity - Initial Velocity) / Time
  • a = (v - u) / t
• It is a vector quantity.
• SI unit: metre per second squared (m/s² or ms⁻²).
• Positive Acceleration: If the velocity increases with time in the direction of motion.
• Negative Acceleration (Retardation or Deceleration): If the velocity decreases with time. The direction of acceleration is opposite to the direction of velocity.
• Zero Acceleration: If the velocity is constant (uniform velocity).
• Uniform Acceleration: If the velocity changes by equal amounts in equal intervals of time. Example: Freely falling body (neglecting air resistance).
• Non-uniform Acceleration: If the velocity changes by unequal amounts in equal intervals of time.

9. Graphical Representation of Motion:

• Distance-Time (d-t) Graphs:

  • Time is plotted on the X-axis, Distance on the Y-axis.
  • Slope of d-t graph gives Speed. (Slope = ΔDistance / ΔTime)
  • Object at rest: Horizontal line parallel to the time axis. (Slope = 0)
  • Uniform speed: Straight line inclined to the time axis. (Constant positive slope)
  • Non-uniform speed: Curved line. (Slope changes)
  • Note: Distance-time graph can never be parallel to the distance axis (implies infinite speed) or have a negative slope (implies distance decreasing with time, which isn't possible for distance).

• Velocity-Time (v-t) Graphs:

  • Time is plotted on the X-axis, Velocity on the Y-axis.
  • Slope of v-t graph gives Acceleration. (Slope = ΔVelocity / ΔTime = (v-u)/t = a)
  • Area under the v-t graph gives the magnitude of Displacement.
  • Uniform velocity (zero acceleration): Horizontal line parallel to the time axis. (Slope = 0)
  • Uniform acceleration: Straight line inclined to the time axis.
    • Positive slope = uniform positive acceleration.
    • Negative slope = uniform negative acceleration (retardation).
  • Non-uniform acceleration: Curved line.
  • Object starting from rest: Graph starts from the origin (u=0).

10. Equations of Motion (for Uniformly Accelerated Motion):
These equations relate initial velocity (u), final velocity (v), acceleration (a), time (t), and distance covered or displacement (s). They are valid ONLY when acceleration 'a' is constant.

• First Equation (Velocity-Time Relation): v = u + at

• Second Equation (Position-Time Relation): s = ut + ½ at²

• Third Equation (Position-Velocity Relation): v² - u² = 2as (or v² = u² + 2as)

  • Derivations: Can be done graphically (using v-t graphs) or algebraically. While derivations might not be directly asked in MCQs, understanding them helps in application.

11. Uniform Circular Motion:

• When an object moves along a circular path with uniform speed (constant magnitude of velocity), its motion is called uniform circular motion.
• Is it accelerated motion? Yes. Although the speed is constant, the direction of motion (and hence velocity) changes continuously at every point on the circle. Since velocity is changing, there must be acceleration.
• This acceleration is called centripetal acceleration, and it is directed towards the center of the circle. (The force causing this is centripetal force).
• Speed Calculation: If 'r' is the radius of the circular path and 'T' is the time taken for one revolution:
  • Distance in one revolution = Circumference = 2πr
  • Speed (v) = Distance / Time = 2πr / T

Key Points for Exams:

• Distinguish clearly between distance/displacement and speed/velocity. Remember which are scalars and vectors.
• Understand the physical meaning of the slope and area under d-t and v-t graphs.
• Know the conditions under which the three equations of motion are applicable (constant acceleration).
• Remember that uniform circular motion is accelerated motion due to the continuous change in direction.
• Be careful with units (convert km/h to m/s by multiplying by 5/18, and m/s to km/h by multiplying by 18/5).

Multiple Choice Questions (MCQs):

1. A particle is moving in a circular path of radius 'r'. The displacement after half a circle would be:
   (a) Zero
   (b) πr
   (c) 2r
   (d) 2πr

2. Which of the following statements is correct regarding velocity and speed of a moving body?
   (a) Velocity of a moving body is always higher than its speed
   (b) Speed of a moving body is always higher than its velocity
   (c) Speed of a moving body is its velocity in a given direction
   (d) Velocity of a moving body is its speed in a given direction

3. The slope of a velocity-time graph gives:
   (a) Distance
   (b) Displacement
   (c) Acceleration
   (d) Speed

4. When a car driver travelling at a speed of 10 m/s applies brakes and brings the car to rest in 20 s, the retardation will be:
   (a) + 2 m/s²
   (b) - 2 m/s²
   (c) - 0.5 m/s²
   (d) + 0.5 m/s²

5. Which of the following graphs represents an object moving with uniform velocity?
   (a) A curved velocity-time graph
   (b) A straight line velocity-time graph parallel to the time axis
   (c) A straight line distance-time graph parallel to the time axis
   (d) A straight line velocity-time graph with a positive slope

6. Suppose a boy is enjoying a ride on a merry-go-round which is moving with a constant speed of 10 m/s. It implies that the boy is:
   (a) At rest
   (b) Moving with no acceleration
   (c) In accelerated motion
   (d) Moving with uniform velocity

7. What does the area under the velocity-time graph represent for a uniformly accelerated motion?
   (a) Initial velocity
   (b) Final velocity
   (c) Acceleration
   (d) Displacement

8. If the displacement of an object is proportional to the square of time (s ∝ t²), then the object moves with:
   (a) Uniform velocity
   (b) Uniform acceleration
   (c) Increasing acceleration
   (d) Decreasing acceleration

9. A body starting from rest travels with uniform acceleration. If it travels 100 m in 5 s, what is the value of acceleration?
   (a) 4 m/s²
   (b) 6 m/s²
   (c) 8 m/s²
   (d) 10 m/s²

10. Which of the following can sometimes be 'zero' for a moving body?
    (i) Average velocity
    (ii) Distance travelled
    (iii) Average speed
    (iv) Displacement
    (a) Only (i)
    (b) (i) and (ii)
    (c) (i) and (iv)
    (d) Only (iv)

Answer Key for MCQs:

1. (c) [Displacement is the shortest distance between initial and final points, which is the diameter = 2r]
2. (d) [Velocity is defined as speed in a specific direction]
3. (c) [Slope = change in velocity / time = acceleration]
4. (c) [u=10m/s, v=0m/s, t=20s. a = (v-u)/t = (0-10)/20 = -0.5 m/s². Retardation is the magnitude, 0.5 m/s²]
5. (b) [Uniform velocity means constant velocity, hence zero acceleration, which corresponds to zero slope on a v-t graph]
6. (c) [In circular motion, direction changes continuously, hence velocity changes, meaning it's accelerated motion]
7. (d) [Area under v-t graph gives displacement]
8. (b) [From s = ut + ½ at², if u=0, s = ½ at². So s is proportional to t² for uniform acceleration starting from rest]
9. (c) [u=0, s=100m, t=5s. Use s = ut + ½ at². 100 = 0*5 + ½ * a * (5)². 100 = 12.5 a. a = 100/12.5 = 8 m/s²]
10. (c) [Displacement can be zero if the object returns to the start. Average velocity (Total Displacement/Time) can also be zero if displacement is zero. Distance and average speed can't be zero for a moving body.]

Study these notes thoroughly. Pay special attention to the graphs and the equations of motion, as they are common sources for questions. Good luck with your preparation!