Kinematics - Physics For Class IX (Science Group) - Question Answers

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Physics For Class IX (Science Group)
UNIT 2: KINEMATICS
Question Answers

Q.1: Define mechanics and its parts.
Ans: Mechanics:
The branch of physics which is related with the study of motion of objects is called Mechanics.
It is divided in two parts

1. Kinematics
2. Dynamics

1. Kinematics:
The word kinematics is derived from Greek word “Kinema” which means motion.
"Kinematics is the branch of Mechanics which deals with motion of objects without reference of force which causes motion."
Example:
An object changes its position in space in a certain time interval without considering the causes of motion.

2. Dynamics:
"Dynamics is the branch of Mechanics which deals with the study of cause of motion."
Example:
Newton's laws of motion

Q.2: (a) Define rest and motion? Or When is a body said to be in the state of rest or in the state of motion?
(b) How are rest and motion are related to each other? Or Describe using examples how objects can be at rest and in motion simultaneously.
Ans(a)REST:
A body is said to be in rest if it does not change its position with respect to its surroundings.
Example:

• In classroom, various things like, table, chairs, books etc all are in state of rest.
• A parking car is in the state of rest with respect to trees and bushes around it.
• A train is stationed at the platform. A person can notice that the train does not change its position with respect to surroundings; hence the train is in a state of rest.

MOTION:
A body is said to be in motion if it changes its position with respect to its surroundings.
Example:

• A train is stationed at the platform. But as soon as the train starts moving its position continuously changing with respect to its surroundings. Now we can say that the train is in motion.

Ans(b): Rest Ans Motion are Relative State:
No body in the universe is in the state of absolute rest or absolute motion. If a body is at rest with respect to some reference point at the same time, it can also be in the state of motion with respect to some other reference point.
For example:

1. A Passenger sitting in a moving bus is at rest because passenger are not changing their position with respect to other passengers or objects in the bus. But for another observer outside the bus noticed that the passengers and objects inside the bus are in motion as they are changing their position with respect to observer standing at the road.
2. Similarly a passenger flying on aeroplane is in motion when observed from ground but at the same times he is at rest with reference to other passengers on board.

Q.3: How many types of motion are there? Define each?
Ans: TYPES OF MOTION:
All objects in universe are in motion. However the nature of their motion is different, some objects move along circular path, other move in straight line while some objects move back and forth only.
There are three types of motion.

1. Translatory motion (linear, circular and random)
2. Rotatory motion
3. Vibratory motion

(1) Translatory Motion:
Definition:
"When all points of a moving body move uniformly along the same straight line, such motion is called translatory motion."
Example:
A train is moving along a straight track, we can observe that every part of the train is moving along that straight path.

Types Of Translatory Motion:
Different objects are moving around in different ways. Following are the three types of translatory motion:

1. Linear Motion:
   We observe many objects moving along straight line.
   Definition:
   "Motion of a body along a straight line is called linear motion."
   Example:
   The motion of a bus in a straight line on road is called linear motion.
   
   
2. Circular Motion:
   Definition:
   "Motion of a body along a circular path is called circular motion."
   Example:
   An artificial satellite moving around the Earth along circular path is an example of circular motion.
   
   
3. Random Motion:
   Definition:
4. "Irregular motion of an object is called random motion."
   Example:
   - The motion of flies, insects and birds. They suddenly change their direction. The path of their motion is always irregular.
   - The motion of butterfly, house fly, dust and smoke particles along zigzag paths are examples of random motion.
   - The motion of the particles of a gas or a liquid known as the Brownian motion which is an example of random motion.

(2) Rotatory Motion:
Definition:
"The motion of the body around a fixed axes which passes through body itself is called spin or rotatory motion."
Example:

1. Motion of fan and spinning top.
   Every point of the top moves in a circle around a fixed axis. Thus every particle of the top possess circular motion. But the top as whole moves around an axis which passes through top itself so the motion of top is rotatory.
2. The motion of a wheel about the axle.
3. The motion of a rider on the Ferris wheel.

are some examples of rotatory motion.

(3) Vibratory Motion:
Definition:
"Back and forth motion of a body about its mean position is called vibratory or oscillatory motion."
Example:
There are many examples of vibratory or oscillatory motion in daily life.

• Motion of child in swing.
  When swing is pulled away from its mean position and then released, the swing start moving back and forth about the mean position. This type of motion is called vibratory or oscillatory motion.
• Motion of the clock’s pendulum.

Q.4: Distinguish between Translatory, Vibratory and Rotatory motion?

S.NO.	Translatory Motion	Rotatory Motion	Vibratory Motion
1.	A body moves along a straight line.	The spinning of a body about its axis.	The body move back and forth about mean position.
2.	Movement of an object from one place to another.	The motion of an object about fixed point.	The body moves up and down.
3.	All particles of the rigid body move with the same velocity at every instant of time.	The motion of a rigid body about a fixed axis. Every particle of body move in a circular path	An object repeat its motion itself.

Q.5: Define the following: 

• Distance
• Displacement
• Speed
• Average speed
• Uniform speed
• Velocity
• Average velocity
• Uniform velocity
• Acceleration
• Uniform acceleration

Ans: 1. DISTANCE:

The total length covered by moving body without mentioning direction of motion is called a distance.

It is denoted by S.
Nature:
It is an scalar quantity.
Unit:
The S.I unit of distance is metre (m).
Example:
A person can use three different paths to move from place A to an other place B. The person covers the distance is either 16 km (purple path) or 24 km (red path).
If a person moves from point 'A' to point 'B' on the curved path then it is called the distance moved by a body.

OR

If a body travels a path 'AB' (Path 1) and return back to point 'A' after taking another path 'BA' (Path 2), then the total distance traveled by a body will be the length of the path.

2. DISPLACEMENT:

The distance covered by a body in a straight line in a particular line or direction is called displacement.

OR

It is the minimum distance covered in particular direction.

It is denoted by d.
Nature:
It is a vector quantity.
Unit:
The S.I unit of displacement is metre (m).
Example:
Actual distance moved by a body from a point 'A' towards point 'B' in a straight line is called displacement.
If the person is back at A then the net displacement becomes zero, as the initial and final points are same.

3. SPEED:
The speed of an object determines that how fast an object is moving. So speed can be define as:

"It is rate of change of position of an object."

OR

"Distance covered by the body in unit time is called speed."

It is denoted by V.  There are many ways to determine speed of an object. These methods depend on measurement of two quantities.

• The distance traveled
• The time taken to travel that distance

Formula:
Thus the average speed of an object can be calculated as:

Speed = distance traveled / time taken

V = S /t

Nature:
Speed is an scalar quantity.

Unit:
Its S.I unit is meter per second (m/s or ms^-1)

4. AVERAGE SPEED:
Average speed can be defined as:
Distance covered by an object in a unit time is called speed.
Formula:
The equation for average speed in symbols can be written as:

V = S/t

Where,
“V” is the speed of the object,
“S” is distance traveled by it and
“t” is time taken by it.

Thus The above equation gives only average speed of the body it can not be said that it was traveling with uniform speed or non uniform speed.
For example:
A racing car can be timed by using a stop watch over a fixed distance say, 500 m. Dividing distance by time gives the average speed, but it may speed up or slow down along the way.

5. UNIFORM SPEED:
An object covers an equal distance in equal interval of time its speed is known as uniform speed.

6. VELOCITY:
Velocity means speed of an object in a certain direction. Thus velocity of an object can be defined as:

"Rate of change of displacement with respect to time is called velocity."

OR

Distance covered by the body in unit time in a particular direction is called velocity.

It is denoted by V.
Formula:

Velocity = Change in displacement/time taken

v = Δd/t

Here,
"d" is displacement of the moving object
"t" is time taken by object and
"v" is velocity.
Nature:
Velocity is a vector quantity.
Unit:
S.I. unit of velocity is meter per second(m/s or ms^-1)

7. AVERAGE VELOCITY:
The velocity of an object is constant when it moves with constant speed in one direction. The velocity of object does not remain constant when it changes direction with out changing its speed, or it changes speed with no change in direction. It can be define as:
Average velocity is the displacement of an object over time.

Formula:
Thus average velocity of an object is given by:

Velocity = total displacement/total time taken

8. UNIFORM VELOCITY:
A body is said to have uniform velocity if it cover equal distance in equal interval of time in a particular direction.

9. ACCELERATION:
An object accelerates when its velocity changes. Since velocity is a vector quantity so it has both magnitude and direction. Thus acceleration is produced when ever:

• Velocity of an object changes
• Direction of motion of the object changes,
• Speed and direction of motion of the object change.

Thus acceleration can be defined as:

Rate of change of velocity of an object with respect to time is called acceleration.

It is denoted by a.
Formula:

Unit:
Acceleration is a vector quantity. Its SI unit is metre per second per second (ms^-2).

Positive Acceleration:
When velocity of an object increases or decreases with passage of time, it causes acceleration. The increase in velocity gives rise to positive acceleration. It means the acceleration is in the direction of velocity.

Deceleration:
Acceleration due to decrease in velocity is negative and is called deceleration or retardation. The direction of deceleration is opposite to that of change velocity.

UNIFORM ACCELERATION:

A body has uniform acceleration, if the velocity of body changes by an equal amount in every equal time period.

When the change i.e., increase or decrease in the velocity of an object is same for every second then its acceleration is uniform. when velocity of an object is increasing by 10 ms^-1 every second, the acceleration is 10 ms^-2. When the velocity of the object is decreasing by 10ms^-1 every second, the deceleration is 10 ms^-2.
Thus, uniform acceleration can be defined as:

A constant rate of change of velocity is called uniform acceleration.

Formula:

Q.6: Define scalar and vector quantities with examples OR Describe type of physical quantities on the basis of information required (existing or has no direction)?
Ans: All physical quantities are divided into two types on the bases of information required to describe them completely.

1. Scalars
2. Vectors

SCALARS:
Definition:

The physical quantities that have magnitude and a suitable unit are called scalar quantities.

OR

Physical quantities, which are completely specified by their magnitude only, are called scalar quantities.

It is denoted by ordinary letter.
For example:

• The mass of a watermelon is 3 kg, where 3 is the magnitude and kg is a suitable unit such quantities are called scalar quantities.
• The other examples of scalar quantities are speed, temperature, mass, density, time, distance, work and energy etc.

VECTORS:
Definition:

The physical quantities which are completely specified by magnitude with suitable unit and particular direction are called as “Vector” quantities.

It is denoted by letter with arrow (→) over them.
For example:

• A bus traveling with a velocity of 50 ms^-1 in the direction of North.
• The other examples of vector quantities are force ,acceleration , momentum, torque and magnetic field, displacement, velocity and weight etc.

Q.7: Define graph and gradients? Describe distance - time and speed time graph?

OR

Plot and interpret distance - time graph and speed - time graph?

OR

Determine and interpret the slope of distance - time and speed-time graph.

OR

Determine from the shape of the graph, the state of a body
(i) at rest
(ii)moving with constant speed
(iii) moving with variable speed
Ans: GRAPH:
A graph is a pictorial way of presenting information about relation between various quantities.
It is a line straight or curved that shows relation between two quantities (variables) out of which one varies as a result of change in other.

Graphical Analysis Of Motion
Graph gives the complete information about the motion of the object based on the measured physical quantities such as distance, speed, time etc.

GRADIENT:
The vertical axis gives rise of the graph while horizontal axis shows its run. The rise divided by run is called gradient.

DISTANCE - TIME GRAPHS

Suppose a bus travels along a straight road from one bus stop to another bus stop. The distance of the bus from first bus stop is measured every second.
The gradient on the distance - time graph is numerically equal to the speed.
The possible motion of the bus is shown by three examples.

1- Uniform Speed:
When bus travels with uniform speed, the distance time graph is a straight line. Graph of the motion of bus with steady speed shows, the line rises 5 m on the distance scale for every 1 seconds on the time scale.
Gradient:

Speed = Distance / time

v = 20 /4 = 5

Thus speed = 5 ms^-1

2- Non-Uniform Speed:
when bus travels with non-uniform speed, the distance time graph is a curve. Fig 2.15(b) shows motion of the bus, for this case the speed rises every second. So the bus covers more distance each second than the one before.

3- Object At Rest:
When the bus stops on the next bus stop to drop or pick the passengers the time continues running but the distance stays same. The graph line is now parallel to the time axis which shows the bus does not change its position .

Conclusion:

1. Uniform Speed: The distance time graph is a straight line. Object cover equal distance in equal interval of time.
2. Non-Uniform Speed: The distance time graph is a curve. Object cover distance with varied speed in a unit time.
3. At Rest: The distance time graph line is parallel to the time axis. Object does not change its position with change of unit time.

SPEED -TIME GRAPH

Speed -time graph tells us that how much speed is increasing or decreasing in every second.
Thus, The gradient on speed - time graph gives the acceleration of the moving object.
If the gradient is positive then acceleration is also positive. On the other hand, if gradient is negative then acceleration will be negative which is known as deceleration or retardation.

1. At Rest (Zero Speed):
The bus is at rest for an interval of 5 seconds. Therefore, speed of bus remains zero for entire interval of time.

2. Uniform Speed:
In graph, the bus moves at steady speed 20 ms-1 for 5 second, so the distance covered is 100 m. The distance is always product of speed and time,
therefore two magnitudes on speed-time graph:

Distance = speed x time

S = v x t

S = (20 X 5 = 100)

Thus distance or area covered is 100 meter
determine the distance represented through shaded rectangle on the graph.

3. Non - Uniform Speed:
Now suppose that once again bus is accelerated as the speed of bus increases at the rate of 10 m every second, the distance covered in next 5 seconds is determined by shaded triangle on the graph.

Area Under speed -time graph:
The area of shaded triangle:

So the distance traveled is 125 meters.
(Note: In book distance traveled is 75 m is given, but according to graph it should be 125 m)
On a speed -time graph, the area under the line is numerically equal to the distance traveled.

Conclusion:

1. At Rest: Object is at rest, so speed is zero. In Speed -Time graph, vertical axis (y-axis) is zero, straight line lies on horizontal axis (x-axis).
2. Uniform speed: Object moves with uniform speed in equal interval of time. In Speed -Time graph, line is parallel to horizontal axis (x-axis).
3. Non - Uniform Speed: Object moves with varied speed in unit of time. In Speed -Time graph, line is straight and start from origin because Object start from rest.

Q.8: Describe first equation of motion?
Ans: FIRST EQUATION OF MOTION:
Suppose a body is moving with uniform acceleration “a” during some time interval “t”, its initial velocity “v_i” changes and denoted as final velocity “v_f ”. It covers a distance “s” in this duration of time.

First equation determines the final velocity of a uniformly accelerated body.
Mathematically:

where,

• v_f = Final Velocity
• v_f = Initial Velocity
• a = acceleration
• t = time

This is known as the first equation of motion.

Q.9: Describe second equation of motion?
Ans: SECOND EQUATION OF MOTION
Suppose a body is moving with uniform acceleration “a” during some time interval “t”, its initial velocity “v_i” changes and denoted as final velocity “v_f ”. It covers a distance “s” in this duration of time.

The second equation of motion determines the distance covered during some time internal “t”, while a body is accelerating from a known initial velocity.
Let us take the

Q.10: Describe third equation of motion?
Ans: THIRD EQUATION OF MOTION
Suppose a body is moving with uniform acceleration “a” during some time interval “t” its initial velocity “v ” changes and denoted as final velocity “v ”. The body covers a distance “s” in this duration of time.
Third equation of motion determines relationship among the velocity and the distance covered by a uniformly accelerated body, where time interval is not mentioned.
Let us take the first equation of motion.

v_f = v_i + at

By squaring the both sides of equation we get:

(v_f)² = (v_i + at)²

Or (v_f)² = v_i² + 2v_iat + a²t²

Therefore

(v_f)² = v_i² + a(S)

2aS = v_f² - v_i²

This is known as third equation of motion for bodies moving with uniform acceleration.

Q.11: Describe the experiment to explain the motion due to gravity or free fall motion? Also define acceleration due to gravity?
Ans: MOTION DUE TO GRAVITY OR FREE FALL MOTION:
Suppose if two stones of different sizes are dropped from same height simultaneously, both stones catch the same acceleration and hit the ground at same time.

Experiment:
To discover the acceleration of free fall bodies of different sizes Galileo Galilee carried out a series of experiments from at leaning tower Pisa and carefully observed that all objects catch the same acceleration due to gravity of earth. The mass or size of object has no effect.

A small feather and a stone are dropped in an air filled tube. Since air resistance greatly affects the feather, so the stone falls faster On the other hand, when feather and stone are dropped in absence of air resistance, they acquire the same acceleration and reach the bottom at same time.

A piece of feather and a piece of stone dropped together in an air filled glass tube (a) and an evacuated air free glass tube (b)

Galileo Experiment Reject Aristotle Claim:
It was against the widely accepted claim of Aristotle that heavier objects would fall faster than lighter one.
Thus acceleration due to gravity  can be define as:
Acceleration Due To gravity:
“When a body falls in such a way that no other force accepts the weight acting on it, then such motion is called free fall motion. Its velocity increases continuously till it strikes the ground and then a body get some acceleration which is called acceleration due to gravity and it is define as follow:

“The acceleration produces in a free falling body due to force of gravity is called acceleration due to gravity.”

Acceleration due to gravity is a constant and it is denoted by "g". Its value near the surface of earth is found to be 9.81 ms^-2. However for ease of calculation value of ‘g’ is approximated to 10 ms^-2.

Negative Gravitational Acceleration
Gravitational acceleration is taken negative for objects moving upward direction. (i.e. -9.8 m/sec²)

Positive Gravitational Acceleration
Gravitational acceleration is taken positive for objects moving downward direction. (i.e. 9.8 m/sec²)

Equation Of Motion For Acceleration Due To gravity
For the motion of bodies under the influence of gravity the equation of motion are slightly modified.
Where,
distance is taken as (S = h) and
acceleration is taken as g (a = g)

There fore equation of motion are taken as.

• (i) v_f = v_i + gt
• (ii) S = v_it + ¹/₂ gt²
• (iii) 2gh = v_f² - v_i²

Short Question Answers

Q.1: Define:

• Motion
  
• Deceleration

Ans: MOTION:
The motion of an object can be described by specifying its position, change in position. speed, velocity and acceleration.

DECELERATION:
Acceleration due to decrease in velocity is negative and is called deceleration or retardation. The direction of deceleration is opposite to that of change velocity.

Q.2: Differentiate with examples between speed and velocity.
Ans: Difference Between Speed And Velocity

Q.3: Give the speed of following animals and objects: White-tailed deer, Ren deer, cheetah, Walking man, Grand prix car, Passenger jet, Sound and Space shuttle
Ans: Average Speed Of Different Animals And Objects:

S.NO.	Animal /Object	Speed (kmh-1)
1.	White-tailed deer	48
2.	Rein deer	60-80
3.	Cheetah	100-120
4.	Walking man	6
5.	Grand prix car	360
6.	Passenger jet	900
7.	Sound	1200
8.	Space shuttle	36000

Q.4: How we can calculate the area under speed-time graph to determine the distance traveled by the moving body.
Ans: Area Under Speed Time Graph:
The area under speed-time graph to determine the distance traveled by the moving body can be calculated by following formula:

Area under speed-time graph = ¹ / ₂ (base x height)

Where,

• The value of base is given on the x-axis.
• The value of height is given on the y-axis

And Area = Distance traveled by a moving body in meter (m).

Q.5: What are equations of motion?
Ans: EQUATIONS OF MOTION:
There are three basic equations of motion for bodies moving with uniform acceleration. These equations are used to calculate the:

• displacement (s),
• velocity (v),
• Time (t) and
• acceleration (a) of a moving body

Types Of  Equation Of Motions:

1. First Equation Of Motion: determines the final velocity of a uniformly accelerated body.
   
   v_f = v_i + at
   
   
2. Second Equation Of Motion: determines the distance covered during some time internal “t”, while a body is accelerating from a known initial velocity.
   
   S = v_it + ¹/₂ at²
   
   
3. Third Equation Of Motion: determines relationship among the velocity and the distance covered by a uniformly accelerated body, where time interval is not mentioned.
   
   2aS = v_f² - v_i²