CBSE Class 9 Science Notes: Motion

Distance and Displacement

Let’s begin our journey into the world of motion! This section dives into the fundamental concepts of distance and displacement, crucial for understanding how objects move.

Definitions:

Distance: The total length of the path traveled by an object. It’s a scalar quantity, meaning it only has magnitude (size).
Displacement: The shortest distance between the initial and final positions of an object. It’s a vector quantity, meaning it has both magnitude and direction.

Core Principles:

Distance can never be negative.
Displacement can be positive, negative, or zero. If an object returns to its starting point, its displacement is zero.
Distance is always greater than or equal to the magnitude of displacement.

Examples:

If you walk 5 meters east and then 3 meters west, your distance traveled is 8 meters (5 + 3), and your displacement is 2 meters east (5 – 3).
If you run around a circular track once and return to your starting point, your distance is the circumference of the circle, but your displacement is 0.

Speed and Velocity

Now, let’s explore how fast objects move! We’ll differentiate between speed and velocity, key concepts in describing motion.

Definitions:

Speed: The rate at which an object covers distance. It’s a scalar quantity.
Velocity: The rate at which an object changes its displacement. It’s a vector quantity, including both speed and direction.

Formulaes:

Speed = Distance / Time
Velocity = Displacement / Time
Average speed = Total distance traveled / Total time taken
Average velocity = Total displacement / Total time taken

Examples:

If a car travels 100 meters in 10 seconds, its speed is 10 m/s. If it travels 100 meters east in 10 seconds, its velocity is 10 m/s east.

Uniform and Non-Uniform Motion

Understanding the patterns of motion is key! We will look at uniform and non-uniform motion.

Definitions:

Uniform Motion: An object covers equal distances in equal intervals of time. Its speed and velocity are constant.
Non-Uniform Motion: An object covers unequal distances in equal intervals of time. Its speed and/or velocity changes.

Characteristics:

Uniform Motion: Constant velocity; the object moves in a straight line with a steady speed.
Non-Uniform Motion: Changing velocity; the object’s speed or direction (or both) changes over time.

Examples:

Uniform Motion: A car moving at a constant speed of 20 m/s on a straight road.
Non-Uniform Motion: A car accelerating or decelerating; a ball thrown upwards.

Acceleration and Its Meaning

Let’s explore acceleration, the rate of change of velocity.

Definitions:

Acceleration: The rate of change of velocity with respect to time. It’s a vector quantity.

Formulaes:

Acceleration (a) = (Final velocity (v) – Initial velocity (u)) / Time (t) or $a = \frac{v – u}{t}$

Meaning:

Positive acceleration indicates increasing velocity (speeding up).
Negative acceleration (deceleration or retardation) indicates decreasing velocity (slowing down).
Zero acceleration means the velocity is constant.

Examples:

A car accelerating from rest.
A car braking to a stop.
An object moving at a constant velocity has zero acceleration.

Distance–Time and Velocity–Time Graphs

Visualizing motion using graphs!

Distance–Time Graphs:

Uniform motion: Straight line (non-zero slope)
Rest: Horizontal line (zero slope)
Non-uniform motion: Curved line (changing slope)

Velocity–Time Graphs:

Uniform motion (constant velocity): Horizontal line
Uniformly accelerated motion: Straight line (non-zero slope)
Non-uniform acceleration: Curved line (changing slope)

Key Points:

The slope of a distance-time graph represents speed/velocity.
The slope of a velocity-time graph represents acceleration.
The area under a velocity-time graph represents the displacement.

Concept of Uniform Circular Motion

Final concept on circular motion!

Definitions:

Uniform Circular Motion: The motion of an object in a circular path at a constant speed.

Core Principles:

Even though the speed is constant, the velocity is changing because the direction is continuously changing.
There is always a centripetal acceleration directed towards the center of the circle.

Examples: