Posted by DHved

Motion - 9th

Motion

Introduction

The world around us is full of moving objects – birds flying, cars running on roads, planets revolving around the Sun, or even the blood circulating inside our body. An object is said to be in motion if its position changes with respect to a fixed point (called the observer) in a given interval of time.
If the position of an object does not change with respect to its surroundings, it is said to be at rest.
Rest and motion are relative. For example, a passenger inside a moving train is at rest with respect to other passengers but is in motion with respect to the trees outside.

Types of Motion

Objects may move in different ways. Some common types are:

  1. Translatory Motion – A body moves from one point to another in a straight or curved path.
    • Rectilinear Motion: Motion along a straight line (e.g., car on a straight road).
    • Curvilinear Motion: Motion along a curved path (e.g., ball thrown in air).
  2. Rotational Motion – When a body rotates about a fixed axis (e.g., Earth spinning on its axis).
  3. Circular Motion – A special type of curvilinear motion where the path is circular (e.g., motion of a satellite around Earth).
  4. Oscillatory Motion – To and fro motion about a mean position (e.g., pendulum, swing).

Distance and Displacement

  • Distance: The total length of the path traveled by an object, irrespective of direction.
    • Scalar quantity (has only magnitude).
    • Always positive.
  • Displacement: The shortest distance between the initial and final position of the object, along with direction.
    • Vector quantity (magnitude + direction).
    • Can be positive, negative, or zero.
Example: A car goes 4 km east and 3 km north.
  • Distance = 4 + 3 = 7 km
  • Displacement = √(4² + 3²) = 5 km (northeast direction)

Speed and Velocity

Speed: The distance traveled per unit time.

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

  • Scalar quantity.
  • Units: m/s (SI).

Velocity: The displacement per unit time.

\( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \)

  • Vector quantity.
  • Direction matters.
  • Units: m/s (SI).
Example: A car moves 100 m east in 20 s.
  • Speed = 100 ÷ 20 = 5 m/s
  • Velocity = 5 m/s east.

Acceleration

  • Acceleration (a): The rate of change of velocity with time.
    \( \text{a} = \frac{\text{𝑣 - 𝑢}}{\text{𝑡}} \)
    Where
    • 𝑣 = final velocity
    • 𝑢 = initial velocity
    • 𝑡 = time
  • If velocity increases → Positive acceleration.
  • If velocity decreases → Negative acceleration (retardation).
    • Unit: m/s²

    Example: A bike increases its velocity from 20 m/s to 40 m/s in 5 s.
    \( \text{a} = \frac{\text{40 - 20}}{\text{5}} \) = 4m/s2

Graphical Representation of Motion

Graphs help us study motion easily.

  1. Distance-Time Graph
    • Straight line → Uniform speed.
    • Curve → Non-uniform speed.
  2. Velocity-Time Graph
    • Straight horizontal line → Uniform velocity.
    • Sloping line → Uniform acceleration.
    • Area under the v–t graph → Displacement.

Equations of Motion

For uniformly accelerated motion, three important equations hold:

  1. First equation: v = u + a t
  2. Second equation: s = u t + 1 2 a t 2
  3. Third equation: v 2 - u 2 = 2 a s

Uniform Circular Motion

When an object moves in a circle at constant speed, its direction changes continuously, hence it is an accelerated motion.

  • Example: Revolution of Earth around Sun, motion of a stone tied to a string and rotated.
  • Acceleration is directed towards the center (centripetal acceleration).
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