Motion Class 9 CBSE Notes – Chapter 8

We do know that matter is composed of particles organized in a certain manner. While the particles in gases are well separated and may move freely, the particles in solids are closely packed, with little space for movement.

CBSE Class 9 Science notes will assist students in studying the topic thoroughly and clearly.

These CBSE Class 9 Science notes were written by subject experts who made the study material very basic, both in terms of language and format.

## Various Terms Related to Motion

**POSITION**

The positioning of an object in relation to a particular point is referred to as its position. The reference point or origin is the point around which the position of an object is defined. It is a vector quantity.

**Unit :** metre ( in SI)

centimetre (in CGS)

**DISTANCE**

The distance travelled by a body is the actual length of the route it takes, regardless of its direction of motion. It is a scalar quantity.

The metric system uses the metre as its SI unit. e.g. Consider the motion of a straight-line object.

Allow the item to begin its motion at point 0 and go through points A, B, and C until it reaches point D.

The entire distance travelled to the object is therefore equal to the real length of the route travelled up to D =OA+ AB+ BC+ CD =5 m+ 10 m+ 8 m+ 20 m=43 m.

**DISPLACEMENT**

Displacement is the change in position of an object when it moves from one position to another.

It is equal to the length of the shortest route between the object’s initial and final positions. As displacement has both magnitude and direction , hence it is a vector quantity.

**Unit :** metre ( in SI)

centimetre (in CGS)

Suppose an object begins at point 0 and travels to location B via A.

The object’s starting location is 0 and its ultimate position is B. Thus, displacement of an object equals the length of the shortest route between its initial and final positions (B).

**DISTANCE VERSUS DISPLACEMENT**

- The displacement of a moving object can never exceed its travel distance. i.e. the displacement < distance ratio is always less than or equal to one.
- When a body travels in a straight line (in a single direction), distance and displacement are identical.
- Although an object’s displacement might be positive, negative, or zero, distance can never be negative or zero.

## Uniform and Non-uniform Motion

**Uniform Motion : **A body is considered to be moving uniformly if it travels similar distances in equal time intervals, regardless of how small these intervals are.

In uniform motion, the distance covered by an object grows linearly as the speed of the object increases.

e.g. When a car travels along a straight line path, it is said to be in uniform motion if it covers equal distances in equal lengths of time at regular intervals.

**Non-Uniform Motion : **If a body travels unequal distances in equal intervals of time, regardless of how small these intervals are, it is said to have non-uniform motion.

For instance, a car moving through a congested market exhibits non-uniform motion.

## Rate of Motion

The rate of motion of an object is defined as the ratio of the distance travelled to the time taken. The terms necessary to quantify the rate of motion are as follows:

**Speed**

The speed of an object is defined as the distance it travels in unit time.

Distance is always the path travelled by the moving body, irrespective of whether the path is straight or curved. Hence, if a body travels a length l in time t,

Speed is a scalar quantity. SI unit of speed is the metre per second (m/s).

Because an object’s distance travelled is either positive or zero, its speed may also be positive or zero but never negative.

Speed may be categorised into the following categories:

**Uniform speed :**When a moving body covers equal distances in equal time intervals, its speed is considered to be uniform, i.e. constant speed.

**Non-uniform speed :**If a moving body travels unequal distances in equal time intervals, its speed is considered to be non-uniform, i.e. variable speed.

**Average speed :**It is defined as the ratio of a body’s total distance travelled to its entire time. Let, u, v and x are the distances travelled by an object in times t1, t2 and t3 respectively, then its average speed = u+v+xt1+t2+t3**Instantaneous speed :**The speed of an object at any moment in time or along its journey is referred to as its instantaneous speed.

For example, the speed of a moving car is measured by a speedometer. At any moment the speedometer reads the instantaneous speed of the car.

**THE SPEED WITH DIRECTION: VELOCITY**

A body’s velocity is defined as its displacement per unit time. i.e. velocity is the rate of movement of an object in a certain direction.

velocity = displacementtime

The term “velocity” refers to a vector quantity. The SI unit of velocity is the metre per second (m/s). An object’s velocity might be positive, zero, or negative.

The velocity of an object may be altered by altering its speed, direction of movement, or both.

Velocity can be classified as:

**Uniform velocity :**If an object travels the same displacements in the same period of time without changing direction, its velocity is said to be uniform, or constant.**Non-uniform velocity :**If an object travels unequal displacements in equal time periods, its velocity is said to be non-uniform, or variable.

A car moving with a constant speed along a curved path has a non-uniform velocity due to its continuous change in direction.**Average velocity :**It is defined as the ratio of the object’s total displacement to the entire time taken.

Average velocity = total displacementtotal time

**Instantaneous velocity :**The velocity of an object at a specific moment in time or along its course is referred to as its instantaneous velocity.

**RATE OF CHANGE OF VELOCITY: ACCELERATION**

When the velocity of a particle increases with time then the particle is said to be accelerated.

The rate of change of velocity with time is called acceleration.

Acceleration = **change in velocity****time**

Acceleration can be classified as:

**Uniform Acceleration :**A uniform acceleration occurs when an item travels in a straight line and its velocity increases or decreases by equal amounts at equal intervals of time.- The way a ball moves as it rolls down an angled plane
- The motion of a freely falling body

**Non-uniform Acceleration :**If an object’s speed goes up or down by different amounts at the same times, it is said to be accelerating in a way that is not uniform.

- The way a car moves on a busy city street.
- How the train moves when it leaves or comes into the station.

## Graphical Representation of Motion

When describing the motion of an object, line graphs might be helpful.

Line graphs are used to demonstrate the relationship between one physical quantity, such as distance or velocity, and another physical quantity, such as time.

**TYPES OF GRAPH**

There are two primary types of graphs that we shall examine:

**DISTANCE-TIME GRAPH**

The change in position of an object over time may be depicted using a suitable scale on the distance-time graph.To create a distance-time graph, time is plotted on the X-axis and the body’s distance is displayed on the Y-axis. The slope of the distance-time graph is equal to the object’s speed in this scenario.

The following sections discuss distance-time graphs under different conditions:

**Distance-Time Graph for Uniform Motion**

If an object travels the same distance in the same amount of time, it moves at an uniform speed.

For uniform speed, the graph of distance travelled vs time is a straight line, as seen in the picture below:

The graphs show that the object travels an identical distance of 4m in an equal length of time, i.e. 2s, indicating that the motion is uniform and the graph is a straight line.

**Distance-Time Graph for Non-uniform Motion**

When a body travels unequal distances in equal time periods, this is referred to as non-uniform motion.

There are two forms of non-uniform motion:

(a) When the body’s speed rises with time, the distance-time graph will have a positive slope, as seen alongside:

The graphs show that the object travels an identical distance of 4m in an equal length of time, i.e. 2s, indicating that the motion is uniform and the graph is a straight line.

The graphs show that at equal intervals of time Over the period of two seconds, the body travels unequal lengths and this gap continues to grow.

That is to say, with the passage of time, the body’s surface area expands and greater distance in the same period of time, i.e. the body’s speed increases.

(b) If the body’s speed decreases with time, the distance-time graph will have a negative slope, as seen below:

The graphs show that the body covers uneven distances in equal periods of time equal to one second and that this distance continues to decrease.

That is, as time passes, the body covers less and less distance in the same amount of time, i.e. the body’s speed decreases.

**Velocity-Time Graph**

The velocity-time graphs show how the velocity of a body changes as time progresses.

A velocity-time graph is created by plotting the velocity of the body along the Y-axis and the time it takes for the body to move along the X-axis. The displacement is represented by the area under the velocity-time plot.

The following are examples of velocity-time graphs under various conditions:

**Velocity-Time Graph for a Body Moving with Constant Velocity**Whenever a body moves with constant velocity, that is, when its motion is uniform, the velocity of that body does not change with the passage of time.

**Velocity-Time Graph for Uniform Accelerated Motion**When moving at a uniform pace, the velocity changes by an equal amount in an equal amount of time interval.

The velocity-time graph in this example is a straight line that passes through the origin.

## Equations of Motion

The relationship between the velocity of a body, its acceleration, and the distance travelled by the body in a given time interval is referred to as the equation of motion.

The following are the three equations of motion:

**Equation for Velocity-Time Relation :**v = u + at

**Equation for Position-Time Relation :**s = ut + 12 at2

**Equation for Position-Velocity Relation :**v2 = u2 + 2as

where u is the initial velocity of the body, a represents its uniform acceleration, v denotes the body’s final velocity after t seconds, and s denotes the distance travelled during this time.

## Uniform Circular Motion

When an object travels in a circular direction at an uniform speed, this is referred to as uniform circular motion.

- When an object travels in a circular route, its direction of motion continually changes.
- Due to the constant change in direction, the velocity varies, and thus motion along a circular route is said to be accelerated.
- When a body completes one circle of a circular route, it travels the distance equal to its circumference, which is 2r, where r is the circular path’s radius.

Then, the speed of a body travelling on a circle route is given by v = 2rt

The following are some instances of circular motion that is consistent:

- A piece of stone attached to a thread and revolved at an uniform speed in a circle.
- The rotation of an electric fan’s blades around the axle.
- The moon’s and earth’s motions.
- A satellite orbiting the earth in a circular orbit.
- A vehicle moves in a circular pattern at a steady speed.

## NCERT questions & answers from Motion

### An object has moved through a distance. Can it have zero displacement ? If yes, support your answer with an example. (CBSE 2015)

**Answer: **Yes, The object’s displacement can be zero. Allow a boy five minutes to finish one round on a circular track. The boy’s journey equals the circumference of the circular track. The displacement of the boy, on the other hand, is 0 because his initial and final positions are identical.

### Distinguish between speed and velocity. (CBSE 2010, 2012, 2013, 2015)

**Answer:**

**Speed :**

- Distance travelled by an object per unit time is known as its speed.
- Average speed of a moving object cannot be zero.
- tells how fast an object moves.
- Speed is a scalar quantity.
- Speed of an object is always positive.

**Velocity : **

- The distance travelled by an object in a particular direction (i.e. displacement) per unit time is known as its velocity.
- Average velocity of a moving object can be zero.
- Velocity tells how fast an object moves and in which direction it moves.
- Velocity is a vector quantity.
- Velocity of an object can be positive or negative.

### Under what conditions) is the magnitude of the average velocity of an object equal to its average speed ? (CBSE 2012, 2013)

**Answer: **When an object moves in one direction along a straight line.

### What does the odometer of an automobile measure ? (CBSE 2010, 2011, 2014, 2015)

**Answer: **Odometer of an automobile measures distance travelled by the automobile.

### What does the path of an object look like when it is in uniform motion ? (CBSE 2012)

**Answer: **Straight path.

### When will you say a body is in uniform acceleration ?

non-uniform acceleration (CBSE 2012, 2013)

**Answer:**

- If a body’s velocity changes by an identical amount at equal time intervals, it has uniform acceleration.
- If a body’s velocity changes unequally across equal time intervals, it has non-uniform acceleration.

### What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis? (CBSE 2010, 2012)

**Answer: **When a distance-time graph is a straight line parallel to the time axis, this indicates that the object’s distance remains constant across time. As a result, the thing remains stationary.

### What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time-axis ?

**Answer: **In this instance, the object’s speed is constant. That is, in a straight line, the object moves equal lengths at equal time intervals. Thus, the object’s motion is uniform.

### What is the quantity which is measured by the area occupied below the velocity-time graph ?

(CBSE 2010, 2012)

**Answer: **Magnitude of the displacement of a body is measured by the area under the velocity-time graph.

### A trolley, while going down an inclined plane has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start ?

**Answer:**

Here, u = 0,v = ?, a = 2 cm s-2, t = 3 s

Using, v = u + at, we get

v = 0 + 2 x 3 = 6 cm s-2.