Class 9 Notes

Class 9 Science Notes Chapter 8 (Motion) – Science Book

Philoid

Philoid

— 7 min read

Science
Alright class, let's focus on Chapter 8: Motion. This is a fundamental chapter in Physics and crucial for many competitive exams. Pay close attention to the definitions, differences between related terms, formulas, and graph interpretations.

Chapter 8: Motion - Detailed Notes for Exam Preparation

1. Introduction: Rest and Motion

  • 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 over time.
  • Motion: An object is said to be in motion if its position changes continuously with respect to a fixed point (reference point or origin) in its surroundings over time.
  • Reference Point (Origin): A fixed point or object with respect to which the position of another object is described. The choice of reference point is crucial; motion is relative. An object can be in motion relative to one reference point and at rest relative to another.

2. Describing Motion: Distance and Displacement

  • Distance:
    • The actual path length covered by a moving object, irrespective of the direction.
    • It is a scalar quantity (has only magnitude, no direction).
    • SI unit: metre (m). Other units: kilometre (km), centimetre (cm).
    • Distance covered is always positive or zero; it can never be negative.
  • Displacement:
    • The shortest distance between the initial and final positions of a moving object, measured in a specific direction.
    • It is a vector quantity (has both magnitude and direction).
    • SI unit: metre (m).
    • Displacement can be positive, negative, or zero.
    • Key Point: If an object returns to its starting point, its displacement is zero, even though the distance covered might be significant. The magnitude of displacement is less than or equal to the distance covered. (|Displacement| ≤ Distance).

3. Types of Motion: Uniform and Non-uniform

  • Uniform Motion:
    • An object is said to be in uniform motion if it travels equal distances in equal intervals of time, no matter how small these intervals may be.
    • In uniform motion, the speed (and velocity, if direction is constant) remains constant.
    • Example: A car moving on a straight road at a constant speed of 40 km/h.
  • Non-uniform Motion:
    • An object is said to be in non-uniform motion if it travels unequal distances in equal intervals of time (or vice-versa).
    • In non-uniform motion, the speed (or velocity) changes over time.
    • Example: A car starting from rest, accelerating, or moving in city traffic.

4. Measuring the Rate of Motion: Speed and Velocity

  • Speed:
    • The rate at which an object covers distance. It tells us how fast an object is moving.
    • Formula: Speed (v) = Distance (s) / Time (t)
    • 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, the average speed is the total distance travelled divided by the total time taken.
    • Formula: Average Speed = Total Distance / Total Time Taken
  • Velocity:
    • The rate at which an object changes its position; it is the speed of an object in a specific direction.
    • Formula: Velocity (v⃗) = Displacement (s⃗) / Time (t)
    • It is a vector quantity.
    • SI unit: metre per second (m/s or ms⁻¹).
    • Velocity can be changed by changing the object's speed, direction of motion, or both.
  • Average Velocity:
    • For non-uniform motion (where velocity changes), the average velocity is the net displacement divided by the total time taken.
    • Formula: Average Velocity = Net Displacement / Total Time Taken
    • If the velocity of an object changes at a uniform rate (uniform acceleration), the average velocity is the arithmetic mean of the initial and final velocities.
    • Formula (uniform acceleration only): Average Velocity = (Initial Velocity (u) + Final Velocity (v)) / 2

5. Rate of Change of Velocity: Acceleration

  • Acceleration:
    • The rate of change of velocity of an object with time. It measures how quickly the velocity is changing.
    • Formula: Acceleration (a) = Change in Velocity / Time Taken = (Final Velocity (v) - Initial Velocity (u)) / Time (t)
    • It is a vector quantity.
    • SI unit: metre per second squared (m/s² or ms⁻²).
  • Types of Acceleration:
    • Positive Acceleration: If the velocity increases with time (e.g., a car speeding up). The direction of acceleration is the same as the direction of velocity.
    • Negative Acceleration (Deceleration or Retardation): If the velocity decreases with time (e.g., applying brakes). The direction of acceleration is opposite to the direction of velocity.
    • Zero Acceleration: If the velocity is constant (uniform velocity).
  • Uniform Acceleration: An object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time. Example: A freely falling body (neglecting air resistance).
  • Non-uniform Acceleration: The velocity changes by unequal amounts in equal intervals of time. Example: A car moving on a crowded city road.

6. Graphical Representation of Motion

Graphs provide a visual way to understand motion.

  • Distance-Time Graphs (s-t graphs):
    • Time is plotted on the X-axis, Distance on the Y-axis.
    • Object at Rest: A straight line parallel to the time axis.
    • Uniform Motion (Constant Speed): A straight line inclined to the time axis. The slope (gradient) of the line gives the speed (Slope = Δs / Δt = Speed). A steeper slope means higher speed.
    • Non-uniform Motion: A curved line. The slope of the tangent at any point on the curve gives the instantaneous speed at that point.
  • Velocity-Time Graphs (v-t graphs):
    • Time is plotted on the X-axis, Velocity on the Y-axis.
    • Uniform Motion (Constant Velocity): A straight line parallel to the time axis.
    • Uniformly Accelerated Motion: A straight line inclined to the time axis.
      • The slope (gradient) of the line gives the acceleration (Slope = Δv / Δt = Acceleration).
      • Positive slope = positive acceleration.
      • Negative slope = negative acceleration (retardation).
      • Zero slope (line parallel to time axis) = zero acceleration (constant velocity).
    • Non-uniformly Accelerated Motion: A curved line.
    • Key Point: The area enclosed between the velocity-time graph and the time axis gives the magnitude of the displacement of the object during that time interval.

7. Equations of Motion by Graphical Method (for Uniformly Accelerated Motion)

These equations relate initial velocity (u), final velocity (v), time (t), acceleration (a), and distance/displacement (s). They are valid only when acceleration is uniform and motion is along a straight line.

  • First Equation (Velocity-Time Relation): v = u + at
    • Derived from the definition of acceleration (a = (v-u)/t) or the slope of the v-t graph.
  • Second Equation (Position-Time Relation): s = ut + ½at²
    • Derived from the area under the v-t graph (Area = Area of rectangle + Area of triangle = ut + ½(v-u)t = ut + ½(at)t = ut + ½at²).
  • Third Equation (Position-Velocity Relation): 2as = v² - u²
    • Derived by eliminating 't' from the first two equations or from the area of the trapezium under the v-t graph (Area = s = ½(sum of parallel sides) × height = ½(u+v)t. Substitute t = (v-u)/a).

8. Uniform Circular Motion

  • When an object moves in a circular path with uniform speed (constant magnitude of velocity), its motion is called uniform circular motion.
  • Important: Although the speed is constant, the direction of motion changes continuously. Since velocity includes direction, the velocity is not constant.
  • Because the velocity changes (due to change in direction), there is acceleration. This acceleration is called centripetal acceleration, and it is always directed towards the centre of the circle. (Note: The calculation of centripetal acceleration is beyond the Class 9 scope, but knowing its existence and direction is important).
  • If an object moves in a circular path of radius 'r' with uniform speed 'v', the time taken to complete one revolution (T) is called the time period.
  • The distance covered in one revolution is the circumference of the circle (2πr).
  • Formula for Speed: v = 2πr / T

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. A car accelerates uniformly from 18 km/h to 36 km/h in 5 seconds. The acceleration is:
    a) 1 m/s²
    b) 5 m/s²
    c) 3.6 m/s²
    d) 18 m/s²

  5. If the displacement-time graph of a particle is parallel to the time axis, the velocity of the particle is:
    a) Unity
    b) Infinity
    c) Zero
    d) Increasing

  6. 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

  7. Which of the following is a vector quantity?
    a) Speed
    b) Distance
    c) Acceleration
    d) Time

  8. When a body moves with uniform velocity, its acceleration is:
    a) Positive
    b) Negative
    c) Zero
    d) Non-uniform

  9. A body is thrown vertically upwards and rises to a height 'h'. The ratio of distance travelled to the displacement is:
    a) 1:1
    b) 2:1
    c) 1:2
    d) Cannot be determined until it returns

  10. An object travels 16 m in 4 s and then another 16 m in 2 s. What is the average speed of the object?
    a) 5.33 m/s
    b) 6 m/s
    c) 4 m/s
    d) 8 m/s

Answers to MCQs:

  1. c) 2r (The shortest distance between starting and ending points after half a circle is the diameter).
  2. d) Velocity of a moving body is its speed in a given direction (Velocity is speed with direction).
  3. c) Acceleration (Slope = change in velocity / time).
  4. a) 1 m/s² (u = 18 km/h = 5 m/s, v = 36 km/h = 10 m/s, t = 5 s. a = (v-u)/t = (10-5)/5 = 1 m/s²).
  5. c) Zero (Displacement is not changing with time, hence the object is at rest, velocity is zero).
  6. d) Displacement (Area under v-t graph gives displacement).
  7. c) Acceleration (Acceleration has both magnitude and direction).
  8. c) Zero (Uniform velocity means no change in velocity, hence zero acceleration).
  9. a) 1:1 (When it reaches height 'h', both distance and displacement are 'h' in the upward direction).
  10. a) 5.33 m/s (Total distance = 16m + 16m = 32m. Total time = 4s + 2s = 6s. Average speed = 32m / 6s = 5.33 m/s).

Make sure you understand the concepts behind each point and formula. Practice numerical problems based on the equations of motion and graph interpretations. Good luck with your preparation!

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