Class 9th || Science || Notes || Chapter 8: Motion

Introduction

Motion is a change in the position of an object with respect to time. Everything in the universe is in a state of continuous motion, from the tiniest particles to massive celestial bodies. In physics, studying the motion of objects involves understanding concepts such as displacement, velocity, acceleration, and time.

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Types of Motion

1. Linear Motion: Movement of an object along a straight path. It can be uniform or non-uniform.

   • Uniform Motion: An object covers equal distances in equal intervals of time. Example: A car moving at a constant speed on a straight road.
   • Non-Uniform Motion: An object covers unequal distances in equal intervals of time. Example: A car speeding up or slowing down.

2. Circular Motion: Movement of an object along a circular path. Example: The motion of the Earth around the Sun.

3. Rotational Motion: Movement of an object around its own axis. Example: The rotation of the Earth around its axis.

4. Periodic Motion: Motion that repeats itself after regular intervals of time. Example: The pendulum of a clock.

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Distance and Displacement

1. Distance:

   • The total length of the path traveled by an object.
   • It is a scalar quantity, meaning it has only magnitude and no direction.
   • Example: If you travel in a straight line from point A to point B, the distance is the length of that line.

2. Displacement:

   • The shortest straight-line distance between the initial and final positions of an object.
   • It is a vector quantity, meaning it has both magnitude and direction.
   • Example: If you move from point A to point B, then back to A, the displacement is zero because you ended up where you started.

Differences between Distance and Displacement:

Distance	Displacement
Scalar quantity	Vector quantity
Always positive	Can be positive, negative, or zero
Depends on the path taken	Depends on the initial and final positions

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Speed and Velocity

1. Speed:
   • The rate at which an object covers distance.
   • It is a scalar quantity.
   • Formula: $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
   • SI Unit: meters per second (m/s).
   • Average Speed: The total distance traveled divided by the total time taken.
2. Velocity:
   • The rate at which an object changes its position (displacement) with respect to time.
   • It is a vector quantity.
   • Formula: $$\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}$$
   • SI Unit: meters per second (m/s).
   • Average Velocity: The total displacement divided by the total time taken.

Differences between Speed and Velocity:

Speed	Velocity
Scalar quantity	Vector quantity
Only magnitude	Magnitude and direction
Can never be negative	Can be positive, negative, or zero

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Acceleration

Acceleration is the rate of change of velocity with respect to time. It describes how quickly an object’s velocity changes.

• Formula:

  $$\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time taken}}$$

  or

  $$a = \frac{v - u}{t}$$

  where:

  • $v$ = final velocity
  • $u$ = initial velocity
  • $t$ = time taken
  • $a$ = acceleration

• SI Unit: meters per second squared (m/s²).

• Uniform Acceleration: If the velocity of an object changes at a constant rate, the acceleration is uniform.

• Non-Uniform Acceleration: If the velocity changes at a varying rate, the acceleration is non-uniform.

Examples:

• A car accelerating from rest to a certain speed has positive acceleration.
• A car slowing down has negative acceleration (also known as deceleration).

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Equations of Motion

The equations of motion are mathematical relationships that describe the motion of an object under uniform acceleration. There are three key equations:

1. First Equation of Motion:

   $$v = u + at$$
   • Where $v$ is the final velocity, $u$ is the initial velocity, $a$ is acceleration, and $t$ is time.

2. Second Equation of Motion:

   $$s = ut + \frac{1}{2} a t^2$$
   • Where $s$ is the displacement, $u$ is initial velocity, $a$ is acceleration, and $t$ is time.

3. Third Equation of Motion:

   $$v^2 = u^2 + 2as$$
   • Where $v$ is the final velocity, $u$ is initial velocity, $a$ is acceleration, and $s$ is displacement.

These equations help solve problems related to uniformly accelerated motion, such as finding velocity, displacement, or acceleration.

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Graphical Representation of Motion

Graphs are an important tool for understanding motion visually.

1. Distance-Time Graph:

   • Slope of the graph gives the speed.
   • A straight line indicates uniform motion.
   • A curved line indicates non-uniform motion.

2. Velocity-Time Graph:

   • Slope of the graph gives acceleration.
   • Area under the curve gives displacement.
   • A straight line indicates constant acceleration.
   • A curved line indicates changing acceleration.

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Uniform Circular Motion

When an object moves in a circular path with constant speed, it is said to be in uniform circular motion. Even though the speed is constant, the velocity changes due to the continuous change in direction. Therefore, an object in uniform circular motion is always accelerating, even if its speed remains unchanged.

• Example: The motion of the Earth around the Sun is an example of uniform circular motion.

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Summary of Key Concepts

1. Motion is the change in position of an object with time.
2. Distance is a scalar quantity, while displacement is a vector quantity.
3. Speed refers to how fast an object moves, while velocity indicates the speed and direction of motion.
4. Acceleration is the rate of change of velocity, and it can be positive (speeding up) or negative (slowing down).
5. The equations of motion provide relationships between velocity, time, acceleration, and displacement.
6. Uniform circular motion involves constant speed but changing velocity due to changing direction.