CBSE Class 9 Science Notes Chapter 8 Motion

Reference Point and Reference Frame

To describe the position of an object, we need a reference point or origin. This reference point is a fixed place or object used to determine if something else is in motion. For example, consider a tree in a park. If you observe a person walking past the tree, you can use the tree as the reference point to determine that the person is moving. A reference frame, or frame of reference, is a coordinate system within which we measure the position, orientation, and other properties of objects. All observations of motion are made relative to this frame of reference. It's crucial to have a common reference frame to make consistent and accurate observations.

Example: Consider a bus moving on the road. A passenger inside the bus sees other passengers as stationary because, within the bus's reference frame, they are not changing their position relative to each other. However, an observer standing outside the bus sees the passengers moving along with the bus. This is because, from the outside observer's reference frame (which is the ground), the position of the passengers is changing as the bus moves.

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In summary, motion can appear differently depending on the chosen reference point and frame of reference. To avoid confusion and ensure consistency in observations, it is essential to establish a common reference frame. This standard frame allows all observers to describe motion in a unified way, facilitating clear communication and understanding of the movement of objects.

Distance and Displacement

Distance

Distance refers to the total length of the path covered by a moving object, regardless of its direction. It is a scalar quantity, which means it only has magnitude and no direction. For example, if you walk 5 kilometers around a park and return to your starting point, the distance covered is 5 kilometers, even though you end up where you started.

Key Points:

• Distance measures the total ground covered by an object.
• It is always a positive value and never zero as long as there is movement.
• It does not take the direction of movement into account.

Displacement

Displacement, on the other hand, is a vector quantity. It measures the shortest distance between the starting point and the final position of an object, considering the direction. Displacement not only has magnitude but also direction. For instance, if you start at point A, walk 3 kilometers east to point B, and then 4 kilometers north to point C, your displacement is the straight-line distance from A to C in a northeast direction.

Key Points:

• Displacement measures the shortest path between the initial and final positions.
• It can be positive, negative, or zero depending on the direction.
• Unlike distance, displacement can be zero if the starting and ending positions are the same.

Difference Between Distance and Displacement

Nature:

• Distance is a scalar quantity (only magnitude).
• Displacement is a vector quantity (magnitude and direction).

Measurement:

• Distance is the total path length covered.
• Displacement is the shortest path between two points.

Value:

• Distance is always positive and never zero if there is any movement.
• Displacement can be positive, negative, or zero.

Example:

If you walk in a circular path and return to your starting point, the distance covered is the circumference of the circle, while the displacement is zero.

Magnitude

Magnitude refers to the size or extent of a physical quantity. In physics, quantities are classified into scalar and vector quantities based on whether they have direction along with magnitude.

Scalar Quantities:

• These are quantities that have only magnitude and no direction.
• Examples include time, distance, mass, temperature, area, and volume.

Vector Quantities:

• These are quantities that have both magnitude and direction.
• Examples include velocity, displacement, weight, momentum, force, and acceleration.

Understanding the difference between distance and displacement, as well as scalar and vector quantities, is fundamental in physics as it helps in accurately describing and analyzing motion.

Velocity is the rate of change of displacement with time. It is a vector quantity, which means it has both magnitude and direction. Unlike speed, which only considers how fast an object is moving, velocity also considers the direction in which the object is moving.

Instantaneous Velocity

Instantaneous velocity is the velocity of an object at a particular moment in time. It represents the rate of change of position for a very small time interval, approaching zero. This can be thought of as the speed and direction of an object at a specific instant. Mathematically, it is defined as the derivative of the position with respect to time.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken for that displacement. It gives an overall sense of the velocity over a given period of time. ​

Comparison of Average Velocity and Instantaneous Velocity:

Average Velocity	Instantaneous Velocity
Defined as the total displacement divided by the total time elapsed.	Defined as the velocity at a particular instant of time.
Calculated by dividing the total displacement by the total time taken.	Calculated by taking the derivative of displacement with respect to time.
Example: If Jack takes 1 hour to travel 10 km from his house to school, his average velocity is 10 km/hr.	Example: While Jack is sitting and waiting for a train to pass, his instantaneous velocity is zero at that moment.

Acceleration

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction. Acceleration occurs in non-uniform motion where the velocity changes over time. The formula for acceleration is:

Acceleration=Change in VelocityTime Acceleration = Time Change in Velocity ​ Or 𝑎=𝑣−𝑢𝑡 a = t v − u ​ where $v$ is the final velocity, $u$ is the initial velocity, and $t$ is the time taken for this change.