KINEMATICS CHAPTER# 02 PHYSICS 9TH – Short / Detailed Question Answers

 PHYSICS 9TH – Short / Detailed Question Answers

KINEMATICS
CHAPTER# 02

Q.1: Define mechanics.
Ans: Mechanics:
The branch of physics which is related to the study of the motion of objects is called Mechanics. It is divided into two parts:
(i) Kinematics
(ii) Dynamics

Q.2: Define kinematics.
Ans: Kinematics:
The word kinematics is derived from the Greek word "Kinema" which means motion. Kinematics is the branch of Mechanics which deals with the motion of objects without reference to force which causes motion.

Q.3: When is a body said to be in the state of rest?
Ans: Rest:
If we have a look around in our classroom, we can observe various things like tables, chairs, books, etc., all are in the state of rest. A car is in a state of rest with respect to trees and bushes around it. Thus, rest can be defined as:

A body is said to be at rest if it does not change its position with respect to its surroundings.

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.

Q.4: Define motion.
Ans: Motion:
When a truck starts moving, its position continuously changes with respect to its surroundings. Now we can say that the truck is in motion. Thus, motion can be defined as:

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

Q.5: How are rest and motion related to each other?
Ans: Rest and motion are related to each other:
No body in the universe is in the state of absolute rest or absolute motion. If a body is in the state of 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, a passenger sitting in a moving bus is at rest because the passenger is not changing their position with respect to other passengers or objects in the bus as shown in the given figure. But for another observer outside the bus, the passengers and objects inside the bus are in motion as they are changing their position with respect to the observer standing at the road.

Similarly, a passenger flying on an aeroplane is in motion when observed from the ground but at the same time, he is at rest with reference to other passengers on board.

Q.6: How many types of motion are there?
Ans: Types of Motion:
We observe around us that all objects in the universe are in motion. However, the nature of their motion is different; some objects move along a circular path, others move in a straight line, while some objects move back and forth only. There are three types of motion:

(i) Translatory motion (linear, circular, and random)
(ii) Rotatory motion
(iii) Vibratory motion

Q.7: Define Translatory Motion.
Ans: Translatory Motion:
Different objects are moving around in different ways. We can observe how various objects are moving. A train is moving along a straight track in the given figure. We can observe that every part of the train is moving along that straight path.

This is called translatory motion. Translatory motion can be defined as:
When all points of a moving body move uniformly along the same straight line, such motion is called translatory motion.

Q.8: Define: (a) Linear motion (b) Circular motion (c) Random motion
Ans:

(a) Linear Motion:
We observe many objects moving along a straight line. The motion of a bus in a straight line on the road is called linear motion. Thus, linear motion can be defined as:
The motion of a body along a straight line is called linear motion.

(b) Circular Motion:
An artificial satellite moving around the Earth along a circular path is an example of circular motion. Thus, circular motion can be defined as:
The motion of a body along a circular path is called circular motion.

(c) Random Motion:
We have observed the motion of flies, insects, and birds. They suddenly change their direction. The path of their motion is always irregular. The random motion can be defined as:
The irregular motion of an object is called random motion.

The motion of a butterfly, housefly, dust, and smoke particles along zigzag paths are examples of random motion. The motion of the particles of a gas or a liquid is known as Brownian motion, which is an example of random motion.

Q.9: Define rotatory motion with examples.
Ans: Rotatory Motion:
If we notice the type of motion of a fan and a spinning top, we will find that every point of the top moves in a circle around a fixed axis. Thus every particle of the top possesses circular motion.

But the top as a whole moves around an axis which passes through the top itself, so the motion of the top is rotatory. Thus rotatory motion can be defined as:
The motion of the body around a fixed axis which passes through the body itself is called spin or rotatory motion. The motion of a wheel about the axle, the motion of a rider on the Ferris wheel are some examples of rotatory motion.

Q.10: What is vibratory motion?
Ans: Vibratory Motion:
If we look at the motion of a child in a swing when the swing is pulled away from its mean position and then released, the swing starts moving back and forth about the mean position. This type of motion is called vibratory or oscillatory motion. Thus vibratory motion can be defined as:
The back and forth motion of a body about its mean position is called vibratory or oscillatory motion.

There are many examples of vibratory or oscillatory motion in daily life. For example, the motion of the clock’s pendulum.

Q.11: How can we describe the motion of an object?
Ans:
The motion of an object can be described by specifying its position, change in position, speed, velocity, and acceleration.

Q.12: Define distance and displacement.
Ans:
A person can use three different paths to move from place A to place B.

• Distance:
  If a person moves from point ‘A’ to point ‘B’ then the total length of the curved path is called the distance moved by the body.

• Displacement:
  Actual distance moved by a body from a point ‘A’ toward point ‘B’ in a straight line (dashed line) is called displacement.

If a body travels a path ‘AB’ and returns back to point ‘A’ after taking another path ‘BA’ (path 2) then the total distance travelled by the body will be the length of the path, however, its displacement will be zero, as the initial and the final points are the same.

Q.13: Define speed, average speed, and uniform speed.
Ans:

• Speed:
  The speed of an object determines how fast an object is moving. It is the rate of change of position of an object. There are many ways to determine the speed of an object. These methods depend on the measurement of two quantities:

  • (i) The distance traveled
  • (ii) The time taken to travel that distance

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

  $$\text{Speed} = \frac{\text{distance traveled}}{\text{time taken}}$$ $$V = \frac{S}{t}$$

  Speed is a scalar quantity and its S.I unit is $ms^{-1}$.

• Average Speed:
  The equation for average speed in symbols can be written as:

  $$V = \frac{S}{t}$$

  where “V” is the speed of the object, “S” is the distance traveled by it, and “t” is the time taken by it.
  Thus, average speed can be defined as: The distance covered by an object in a unit time is called speed.

  Uniform Speed:
  The above equation gives only the average speed of the body; it cannot be said that it was traveling with uniform speed or non-uniform speed. For example, a racing car can be timed using a stopwatch over a fixed distance, say 500m.
  Dividing distance by time gives the average speed, but it may speed up or slow down along the way. An object that covers an equal distance in an equal interval of time has uniform speed.

  
  

Q.14: Define velocity, average velocity, and uniform velocity.
Ans:

• Velocity:
  Velocity measures the speed of an object in a certain direction. Velocity is a vector quantity.
  Thus, the velocity of an object can be defined as:

  $$\text{Velocity} = \frac{\text{change in displacement}}{\text{time taken}}$$ $$V = \frac{\Delta d}{t}$$

  Here, $d$ is the displacement of the moving object. It is the time taken by the object, and $V$ is velocity. The S.I unit of velocity is $ms^{-1}$.

• Average Velocity:
  The velocity of an object is constant when it moves with a constant speed in one direction. The velocity of an object does not remain constant when it changes direction without changing its speed, or it changes speed with no change in direction. Thus, the average velocity of an object is given by:

  $$\text{Velocity} = \frac{\text{total displacement}}{\text{total time taken}}$$

• Uniform Velocity:
  A body is said to have uniform velocity if it covers equal distances in equal intervals of time in a particular direction.

Q.15: Define acceleration and uniform acceleration.
Ans:

Acceleration:
An object accelerates when its velocity changes. Since velocity is a vector quantity, it has both magnitude and direction. Thus, acceleration is produced whenever:

1. Velocity of an object changes.
2. Direction of motion of the object changes.
3. Speed and direction of motion of the object change.

Thus, acceleration can be defined as:
The rate of change of velocity of an object with respect to time is called acceleration.

$$\text{Acceleration} = \frac{\text{change in velocity}}{\text{time taken}}$$ $$a = \frac{\Delta v}{t} \quad \therefore \quad \Delta v = v_f - v_i$$ $$a = \frac{v_f - v_i}{t}$$

Acceleration is a vector quantity. Its S.I. unit is meter per second square $(\text{ms}^{-2})$.
When the velocity of an object increases or decreases with time, it causes acceleration. The increase in velocity gives rise to positive acceleration, meaning the acceleration is in the direction of velocity. Whereas, acceleration due to a decrease in velocity is negative and is called deceleration or retardation. The direction of deceleration is opposite to that of velocity.

Uniform Acceleration:
A body has uniform acceleration if the velocity of the 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 the same for every second, then its acceleration is uniform. For example, when the velocity of an object is increasing by $10 \, \text{ms}^{-1}$, it has uniform acceleration. When the velocity of the object is decreasing by $10 \, \text{ms}^{-2}$ every second, the deceleration is $10 \, \text{ms}^{-2}$.

Thus, uniform acceleration can be defined as:
A constant rate of change of velocity is called uniform acceleration.
The uniform acceleration can be calculated by using the following formula:

$$a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t_2 - t_1}$$

Where:
$V_i$ = Initial velocity (in $\text{ms}^{-1}$)
$V_f$ = Final velocity (in $\text{ms}^{-1}$)
$t_1$ = Time at which an object is at initial velocity (in sec)
$t_2$ = Time at which an object is at final velocity (in sec)
$\Delta v$ = Change in velocity (in $\text{ms}^{-1}$)
$\Delta t$ = Time interval between $t_1$ and $t_2$ (in sec)

Q.16: Explain scalar and vector quantities.
Ans:

All physical quantities are divided into two types based on the information required to describe them completely:

1. Scalars
2. Vectors

Scalars:
There are certain physical quantities that can be described through their magnitude and a suitable unit. This information is enough to describe them. For example, the mass of a watermelon is 3kg, where 3 is the magnitude and kg is a suitable unit. Such quantities are called scalar quantities. Thus, we can define scalar quantities as:
The physical quantities that have magnitude and a suitable unit are called scalar quantities.
Other examples of scalar quantities are speed, temperature, mass, density, etc.

Vectors:
Some physical quantities need direction along with their magnitude and unit for their complete description. For example, a bus traveling with a velocity of 50 $\text{ms}^{-1}$ in the direction of the north. Vector quantities can be defined as:
The physical quantities which are completely specified by magnitude with a suitable unit and particular direction are called “vector” quantities.
Force, acceleration, momentum, torque, and magnetic field are examples of vector quantities.

Q.17: How can we represent a vector quantity?
Ans:
Representation of Vector:
A vector diagram is an easy way to represent a vector quantity. The directed line segment can be used to represent a vector. The length of the line segment gives the magnitude of the vector, and the arrowhead gives its direction. For example, the given figure represents the velocity of a car traveling at $50 \, \text{ms}^{-1}$ in the direction of $30^\circ$ North of East.

Q.18: Describe distance–time and speed–time graphs.
Ans:
Graphs give complete information about the motion of the object based on the measured physical quantities such as distance, speed, time, etc.

Distance–Time Graphs:
A bus travels along a straight road from one bus stop to another bus stop. The distance of the bus from the first bus stop is measured every second. The possible motion of the bus is shown by three examples:

1. Fig (a) – Uniform Speed: Shows a straight line, indicating constant speed.
2. Fig (b) – Non-uniform Speed: Shows a curve, indicating changing speed.
3. Fig (c) – Object at Rest: Shows a horizontal line, indicating no movement.

The vertical axis shows the distance, while the horizontal axis shows time. The rise divided by the run is called the gradient. The gradient on the distance–time graph is numerically equal to speed. When a bus travels with uniform speed, the distance–time graph is a straight line. For example, in Fig (a), the line rises $5 \, \text{m}$ on the distance scale for every $1 \, \text{s}$ on the time scale.

Gradient Calculation:

$$\text{Gradient} = \frac{20}{4} = 5$$

Thus, the speed is $5 \, \text{ms}^{-1}$.

Continuation of Q.18:
When a bus travels with non-uniform speed, the distance–time graph is a curve. Fig (b) shows the motion of the bus; for this case, the speed rises every second. So the bus covers more distance each second than the one before.

When the bus stops at the next bus stop to drop or pick up passengers, the time continues running, but the distance stays the same. The graph line is now parallel to the time axis, which shows the bus does not change its position (Fig C).

Speed–Time Graph:
Speed–time graphs tell us how much speed is increasing or decreasing every second. Thus, the gradient on the speed–time graph gives the acceleration of the moving object.

• If the gradient is positive, then the acceleration is also positive.
• If the gradient is negative, then acceleration will be negative, which is known as deceleration or retardation.

In the graph (Fig a), the bus is at rest for an interval of 5 seconds. Therefore, the speed of the bus remains zero the entire time.

In Fig (b), the bus moves at a steady speed of $20 \, \text{ms}^{-1}$ for 5 seconds, so the distance covered is $100 \, \text{m}$. The distance is always the product of speed and time. Therefore, two magnitudes on the speed–time graph ($20 \times 5 = 100$) determine the distance represented through the shaded rectangle on the graph (Fig b).

Now suppose that once again the bus is accelerated as the speed of the bus increases at the rate of $5 \, \text{m/s}^2$ every second; the distance covered in the next 5 seconds is determined by the shaded triangle on the graph (Fig c).

The area of the shaded triangle is $\frac{1}{2} (\text{base} \times \text{height})$. So the distance traveled is $75 \, \text{meters}$. On a speed–time graph, the area under the line is numerically equal to the distance traveled.

Q.19: Describe the first equation 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.

Suppose a body is moving with uniform acceleration “a” during some time interval “t.” Its initial velocity “Vi” changes and is denoted as final velocity “Vf.” It covers a distance “S” in this duration of time.

First Equation of Motion:
The first equation of motion determines the final velocity of a uniformly accelerated body.

Where:

• $V_f$ = final velocity
• $V_i$ = initial velocity
• $a$ = acceleration
• $t$ = time

The average acceleration is the change in velocity over a time interval.

$$a = \frac{\text{change in velocity}}{\text{time}}$$ $$a = \frac{V_f - V_i}{t}$$ $$at = V_f - V_i$$ $$V_f = V_i + at$$

This is known as the first equation of motion.

Q.20: Explain the second equation of motion.
Ans: The Second Equation of Motion:
The second equation of motion determines the distance covered during some time interval “t,” while a body is accelerating from a known initial velocity.

As we know the average velocity:

$$\text{Average velocity} = \frac{V_f + V_i}{2}$$

From the first equation of motion, we know that $V_f = V_i + at$. Putting this value of $V_f$, we get:

$$\text{Average velocity} = \frac{(V_i + at) + V_i}{2}$$ $$= \frac{V_i + at + V_i}{2}$$ $$= \frac{2V_i + at}{2}$$ $$= V_i + \frac{1}{2} at$$

As the $S = vt$ or $v = \frac{S}{t}$, the above equation becomes:

$$\frac{S}{t} = V_i + \frac{1}{2} at$$ $$\therefore S = V_i t + \frac{1}{2} at^2$$

This equation is known as the second equation of motion.

Q.21: Derive the third equation of motion.

Ans: The Third Equation of Motion:

The third equation of motion determines the relationship between the velocity and the distance covered by a uniformly accelerating body, where the time interval is not mentioned.

Let us take the first equation of motion:

$$V_f = (V_i + at)$$

By squaring both sides of the equation, we get:

$$V_f^2 = (V_i + at)^2$$ $$V_f^2 = V_i^2 + 2V_i at + a^2 t^2$$ $$V_f^2 = V_i^2 + 2a(V_i t + \frac{1}{2} a t^2) \quad \text{(1)}$$

According to the second equation of motion:

$$S = V_i t + \frac{1}{2} a t^2$$

Therefore, equation (1) becomes:

$$V_f^2 = V_i^2 + 2a(S)$$ $$2aS = V_f^2 - V_i^2$$

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

Q.22: Describe the motion due to gravity.

Ans: Motion Due to Gravity:

If two stones of different sizes are dropped from the same height simultaneously, we can observe that heavier and lighter stones catch the same acceleration and hit the ground at the same time.

To discover this, Galileo Galilei carried out a series of experiments from the Leaning Tower of Pisa and carefully observed that all objects catch the same acceleration due to the gravity of the Earth. The mass or size of the object has no effect.

It was against the widely accepted claim of Aristotle that heavier objects would fall faster than the lighter ones. A small feather and a stone are dropped in an air-filled tube. Since air resistance greatly affects the feather, the stone falls faster.

On the other hand, when a feather and a stone are dropped in the absence of air resistance, they acquire the same acceleration and reach the bottom at the same time.

Acceleration due to gravity ‘g’ is a constant. Its value near the surface of the earth is found to be 9.81 m/s². However, for ease of calculation, the value of ‘g’ is approximated to 10 m/s².

Gravitational acceleration is taken negative for objects moving downward and positive for objects moving upward. For the motion of bodies under the influence of gravity, the equations of motion are slightly modified. Where distance is taken as (S=h) and acceleration is taken as g (a = g).

Therefore, equations of motion are taken as:

(i) $V_f = V_i + gt$

(ii) $h = V_i t - \frac{1}{2} gt^2$

(iii) $2ah = V_f^2 - V_i^2$