**Class 9 Science Chapter 8 Notes Motion**

**CBSE Class 9 Science Chapter 8 Notes Motion** **on this step-by-step Motion answer guide . In some of State Boards and CBSE schools, students are taught thru NCERT books. As the chapter comes to an end, students are requested few questions in an exercising to evaluate their knowledge of the chapter. Students regularly want guidance dealing with those NCERT Class 9 Science Chapter 8 Notes Motion. **

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**Chapter 8 : Motion**

**Motion:** A body is said to be in motion when its position change continuously with respect to its surrounding.

**Rest: **A body is said to be in rest when its position does not change continuously with respect to its surrounding.

## Describing Motion/Reference point

Reference point: A reference point used to describe the position of objects, is called the origin.

Example: Assume that a school in a village is 2km north of the railway station. The position of the school with respect to the railway station. In this example the railway station is the reference point.

Example: A farmer standing in his field near the track perceives the train and passengers sitting in it as moving. However, a passenger inside the train sees his fellow passengers to be at rest.

- In order to make observations easy, a convention or a common reference point or frame is needed. All objects must be in the same reference frame.

## Type of motion

There are three type of motion:

- Translatory motion
- Rotatory motion
- Vibratory motion

**Translatory motion**

- In translatory motion the particle moves from one point to another. This Motion may be along a straight line or along a curved path.
- Motion along a straight line is called rectilinear motion.
- Motion along a curved path is called curvilinear motion.
- Example: A car moving on a straight road.

**Rectilinear motion**

Example: A car negotiating a curve.

**Curvilinear motion**

**Rotatory motion**

In rotatory motion, the particles of the body describe concentric circle about the axis of motion.

**Vibratory Motion**

In vibratory motion the particles moves to and fro about a fixed point.

## Distance and Displacement, Magnitude

The simplest type of motion is the motion along straight line.

**Distance:** Total path length covered by an object during a given time period from its initial position to final position that is known as distance.

- Distance does not depend upon the direction of motion.

EXAMPLE: Let consider the motion of an object moving along a straight path. The object starts its reference point. Let A,B and c represent the position of the object at different instants. At first the object moves through C and B and reaches A. Then it moves back along the same path and reaches C through B. The total path length covered by the object is OA +AC, that is 60 km +35km = 95 km. this is the distance covered by the object.

**Displacement: **The shortest distance measured from the initial position to the final position of an object is known as the displacement.

- Displacement has magnitude as well as direction.

EXAMPLE: Let motion of the object from o to a the distance covered is 60 km and the magnitude of displacement id=s also 60 km. during its motion from o to a and back to b, the distance covered = 60 km add 25 equal to 85 km while the displacement equal to 35 km

- The displacement for a course of motion may be zero but the corresponding distance covered is not zero. If we consider the object to travel back to O , the final position concides with the initial position, and therefore , the displacement is zero.
- Under no condition , displacement of an object can be more than the distance covered by it.

**Magnitude: **Magnitude described in simple word as distance or quantity. It is used to describe the size or extent of something.

- The numerical value of any physical quantity is its magnitude.

### ** Scalar quantities and Vector quantities**

Scalar quantities | Vector quantities |

Scalar quantities: physical quantities which are described by specifying their numerical value(or magnitude) only are called scalar quantities or scalars. | Vector quantities: Quantities which are described by specifying their magnitude as well as direction are called vector quantities or vectors. |

Distance is a scalar quantities. | Displacement is a vector quantities. |

E.g: time, distance, mass, temperature, area, volume | E.g: Velocity, displacement, weight, momentum, force, acceleration, etc. |

### Difference between Distance and Displacement

DISTANCE | DISPLACEMENT |

Distance is the total path length covered by an object during a given time. | Displacement during a given time is the shortest distance measured from initial position to final position of the object. |

Distance has a magnitude only and no direction. Thus distance is a scalar. | Displacement is characterised by its magnitude as well as direction. Thus, Displacement is a vector. |

Distance is always taken positive | Displacement can be positive or negative or even zero. |

Distance can never have a magnitude less than that of Displacement | Magnitude of displacement is either equal to or less than that of distance covered during the same time. |

### Uniform motion and non uniform motion

**Uniform Motion**

An object is said to be in uniform motion if it covers exactly the same distance is equal intervals of time.

Example Let consider an object moving along a straight line and covering 5 m in the 1^{st} second, 5m in the 2^{nd} second, 5m in the 3^{rd} second and so on. The object is in a state of union motion.

**Nonuniform motion**

An object is said to be in a nonuniform motion if it covers unequal distance in equal interval of time or equal distance in unequal interval of time.

Example: let consider a truck moving on agro Mumbai highway. The total distance covered by the truck in five hours of its continuous motion is given in the table. From the table, we conclude that in successive five hours, the truck has covered distance of 40km, 60km,50km,60km and 80 km respectively. As distance covered by the truck are different in equal interval of time, the motion of the truck is nonuniform motion.

**Measuring the rate of motion:**

During motion, object may take different time to cover a given distance . some object may move fast but some other object may move slowly. To identify slow or fast motion.

To define this term known a speed. Speed of a moving object is the distance travelled by it in unit time.

## Speed

**Speed, v = Distance/Time = s\t**

**Unit of Speed**

SI unit of speed is meter per second (m/s).

The speed is measured in centimetre per second ( cm/s)

The speed is commonly measured in kilometre per hour.

- Speed is a scalar quantity

**Types of speed**

There are mainly four type of speed

**Uniform speed or Constant speed**- If a moving object covers equal distance in equal interval of time. Then the speed of object is said to be uniform speed or constant speed.

**Nonuniform speed or variable speed**- If a moving object covers unequal distances in equal intervals of time or equal distances in unequal intervals of time, then the speed of the object is said to be nonuniform speed or variable speed.

**Average speed**- The average speed of a moving object is defined as the ratio of total distance travelled by the object to the total time taken to cover that distance.

- Instantaneous speed
- The speed of an object at a particular instant during its motion is called its instantaneous speed.

Speed with direction: velocity

## Velocity

Speed of an object gives its magnitude of rate of motion but it does not tell anything about direction of motion. If we specify the direction of motion then concept of motion become more comprehensive. For this purpose we define a new term velocity.

Velocity of an object is its speed moving in a particular direction.

Velocity, v = displacement (s)/ Time (t)

- Velocity is a vector quantity.

**Unit of velocity**

Velocity is defined as displacement per unit time

Unit of velocity = Unit of displacement/ Unit of time

- SI Unit of velocity is metre/second (m/s)
- For moving vehicles, Velocity is generally expresses in kilometre/hour (km h–1)

**Type of Velocity**

There are mainly three types of velocity.

- Uniform Velocity or Constant Velocity
- If a moving object covers equal displacement in equal intervals of time then the velocity of the object is said to be uniform Velocity or constant velocity.

- Nonuniform velocity or variable velocity
- The velocity of an object is said to be nonuniform of it covers unequal displacements in equal interval of time.

- Average velocity
- For object having nonuniform velocity, we define the average velocity ad the ratio of total displacement of the object and total time for that.
- Average velocity , vav = Total displacement/ Total time

In case the velocity of an object Moving along a straight line is changing at a uniform rate, the average velocity of the object is given by the arithmetic mean of initial velocity and final velocity for a given time interval.

- Average velocity, vav = Initial velocity + final velocity/2

Vav = u+v/2

### Difference between speed and velocity

SPEED | VELOCITY |

Speed is defined as the distance covered per unit time. | Velocity is defined ad the displacement covered per unit time. |

Speed is an object tells us how fast does it move. | Velocity of an object tells us how fast and in which direction the given object moves. |

Speed of an object is a scalar and is always positive. | Velocity of an object is a vector and can be positive or negative. |

The average speed of a moving object is always finite and cannot be zero. | The average velocity of a moving object can be zero too. |

## Rate of change of velocity ( The acceleration)

During uniform motion along a straight line, the velocity of an object remain constant and it does not change with time. In nonuniform motion, the velocity of the object varies. The velocity may have different value at different instants of time as well at different points of the path and hence, change in velocity of the object during a given time interval is not zero. For such a situation we, define the term acceleration.

The acceleration of an object is a measure of the change in the velocity of an object per unit time.

Acceleration = change of velocity/Time taken

**Mathematical Expression for acceleration**

If the initial velocity of an object changes from an initial value u to the final value v in the time t, the acceleration a.

- Change in velocity = final velocity – initial velocity = v – u
- Acceleration of the object, a = change in velocity/Time = v – u/t

**Unit if Acceleration**

Acceleration is defined ad the rate of change in velocity.

- Unit of acceleration = Unit of change in velocity/Time = Unit of velocity/Time
- The SI unit of acceleration is metre/(second)^2,
- It is generally expressed as m/s^2.

**Positive and Negative Acceleration**

- The acceleration of an object is said to be positive if the direction of an acceleration is same as the direction of the velocity.
- The acceleration of an object is said to be negative if the direction of acceleration is opposite to the direction of velocity.

**Examples of positive and negative acceleration**

- When a rocket lifts up from the ground, its acceleration is positive and it is speeded up.
- When a paratrooper opens his parachute, his speed decreases as he approaches the ground. The acceleration is negative.

Acceleration is a vector

The acceleration has magnitude as well as direction of its own, hence acceleration is a vector quantity.

**Uniform Acceleration**

If an object travels in a straight line and its velocity change (either increase or decreases) by equal amounts in equal intervals of time, then the acceleration of the object is said to be uniform.

**Nonuniform Acceleration**

If the velocity of an object change (either increase or decreases) by unequal amount in equal intervals of time, Then the acceleration of the object is said to be nonuniform or variable.

**Graphical representation of motion**

A Graph is one of the commonly employed tools used to describe the motion of an object. From a distance – time graph, we can calculate the speed of an object and form a velocity – time graph, we can calculate the acceleration of the moving object. From a velocity – time graph we can calculate distance covered by the object in a given time.

- Distance – time graph

Distance time graph shown the variation of distance covered by an object with time.

- Distance time graph for an object at rest

An object at rest, the distance time graph is a straight line AB parallel to the time axis

- Distance time graph of an object in uniform motion along a straight line

For uniform motion along a straight line, the distance is a straight line OAB, which is inclined at a constant angle from the time axis.

- Distance time graph of an object in nonuniform motion

The motion of an object is said to be nonuniform if it covers unequal distance in equal intervals of time.

For nonuniform motion, slope of distance time graph varies from point to point.

- Velocity Time graph

For an object travelling along a straight line, the velocity time graph tells us the variation of its velocity with time.

- Velocity time graph for a uniform motion

For a uniform motion of an object along a straight line, the velocity of the object remains unchanged and it does not change with time.

- Determination of the distance covered in a given time

From velocity time graph, the magnitude of the displacement can be easily determined by the area enclosed by the velocity time graph and the time axis.

- Velocity time graph for uniformly accelerated motion [When the object is initially at rest]

Let an object start moving from rest and its motion is uniformly accelerated along a straight line. Then, magnitude of the velocity of the object goes on increasing uniformly with time . thus, magnitude of velocity is directly proportional to time, v ∝ t.

For a uniformly accelerated motion, the slope of velocity time graph gives the value of uniform acceleration of the moving object.

- Velocity time graph for uniformly Accelerated motion (when the initial velocity of the object is finite)

The velocity time graph is a straight line inclined to the time axis but the straight line does not pass through the origin.

- Velocity time graph for uniformly retarded motion

Let an object start moving along a straight line with an initial velocity u and under a uniform negative acceleration. For such a motion, the velocity of the object regularly goes on falling with time and finally the object comes to a rest.

- Velocity time graph for nonuniformly Accelerated motion

Let an object start moving along a straight line but the acceleration of the object is

Nonuniformly. In such aa situation, the velocity of a moving object does not rise or fall uniformly with time.

## Equations of motion or Equations of motion by graphical method

For uniformly accelerated motion of an object along a straight line, we can easily correlate its velocity, acceleration and the distance covered by it in a given time interval by set of three equations. These equations are known as the equations of motion.

- Velocity time relation: Let an object start moving with an initial velocity u and during its motion under uniform acceleration a, the final velocity of the object become v after a time t, then as per velocity time relation.

** V = u + at**

- Position time relation: Let an object start moving with an initial velocity u and has a uniform acceleration a. Then, total distancer s (or magnitude of displacement) covered by the object in time t is given by position time relation.

** S = ut + 1/2at^2**

- Position velocity relation: Let an object start moving along a straight line with a constant acceleration a such that its velocity change from u to v while covering a distance s, then as per position velocity relation.

** V^2 – u^2 = 2as**

Derivation of velocity time relation by graphical method

The velocity time graph for uniformly accelerated motion along a straight line is shown.

** V = u + at or at = v – u**

Derivation of position time relation by graphical method

Consider the velocity time graph for a uniformly accelerated motion along a straight line shown in.

** S = ut + 1/2at^2**

Derivation of position velocity relation by graphical method

Consider the velocity time graph for a uniformly accelerated motion along a straight line, which is shown.

** v^2-u^2 = 2as**

**Uniform circular motion**

The motion of an object along a circular path around a fixed point is known as the circular motion.

Example: electric fan, motion of the moon around the earth.

Motion of an object in a circular path with a uniform speed is called uniform circular motion.

In uniform circular motion, velocity is continuously changing

In uniform circular motion, the speed of a moving object remains constant but velocity of the object continuously changing in its direction of motion.

**Revolution period**

The time taken by an object, undergoing uniform circular motion, to complete one revolution along the circular path is called its revolution period.

Revolution period, T = Total distance covered in one revolution/Constant speed

** T = 2πr/v**

**Difference between uniform linear motion and uniform circular motion**

Uniform linear motion | Uniform circular motion |

The object is travelling along a straight line path in a given direction. | The object moves along a circular path around a fixed point. |

The direction of motion does not change. | The direction of motion changes continuously. |

Speed as well as velocity remain unchanged and there is no acceleration. | Speed remains constant but velocity changes continuously due to change in direction. Hence it is an accelerated motion. |

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