9th Class Physics Unit 2 Kinematics Long Questions and Answers

1.Define mechanics and also Differentiate between the two main branches of mechanics.

Mechanics Mechanics is the branch of physics that deals with the motion of objects and the forces that cause or change this motion. It helps us study and predict how objects behave when in motion or when forces are applied to them.

Two Main Branches of Mechanics:

i. Kinematics:
Kinematics is the study of motion without referring to the forces that cause it. It focuses on describing how objects move by examining parameters like displacement, velocity, acceleration, and time.

Example Describing the motion of cars, buses, or motorcycles moving on the road without considering what causes them to move.

ii. Dynamics:
Dynamics deals with the study of forces and their effect on the motion of objects. It explains why an object moves and considers the forces that cause or change this motion.

Example The motion of an object falling from a table to the ground by analyzing the force of gravity acting on it.

2.Differentiate between scalar and vector quantities with examples.

Scalars A scalar is a physical quantity that can be described completely by its magnitude only. Magnitude includes a number and an appropriate unit. For example, when we ask a shopkeeper for 5 kilograms of sugar, the shopkeeper fully understands the quantity we want based solely on the magnitude of the mass.

Examples Mass, length, time, speed, volume, work, energy, pressure, and power etc.

Addition of Scalars Scalar quantities can be added using simple arithmetic operations. For example:
5 meters+3 meters=8 meters

Vectors A vector is a physical quantity that requires both magnitude and direction to be described completely.

Examples Velocity, displacement, force, momentum, torque, acceleration, and weight etc.

Addition of Vectors Vectors cannot be added like scalars because vector quantity need magnitude and direction. Vector quantities are added by head to tail rule.

Importance in Kinematics Understanding the distinction between scalars and vectors is very important in kinematics because motion involves both the magnitude and direction of quantities like velocity and displacement. While scalar quantities describe "how much," vector quantities describe "how much and in which direction." This distinction helps accurately describe and analyze the motion of objects.

3.How are vectors represented symbolically and graphically? Explain.

Symbolic Representation of Vectors Vectors are represented in textbooks using boldface letters, such as A, V, F, and d. However, when writing by hand, vectors are denoted with a small arrow over the letter, like A, v, F and d. The magnitude of a vector is shown using the same letter without the arrow, written in italics, such as A, V, F and d.

Graphical Representation of Vectors Vectors can be represented graphically by drawing a straight line with an arrowhead at one end.

Magnitude The length of the line corresponds to the vector's magnitude, determined according to a suitable scale.

Direction The arrowhead indicates the vector's direction.

Reference Axes for Direction To define the direction of a vector, we use two mutually perpendicular lines:

Horizontal Line Represents the east-west direction and is called the x-axis.

Vertical Line Represents the north-south direction and is called the y-axis.

These axes intersect at a point called the origin, denoted as O.

Figure 2.1(a) illustrates two mutually perpendicular lines representing the east-west and north-south directions.

Drawing Vectors on Axes Vectors are usually drawn starting from the origin of the reference axes and extending toward the specified direction. The direction is defined by an angle θ (theta) with respect to the x-axis.

Figure 2.1(b) Shows the x-axis (horizontal) and y-axis (vertical) intersecting at the origin (O). A vector is drawn starting from this origin, and its direction is indicated by an angle θ with respect to the x-axis.

Measurement of Angle θ

The angle θ is measured from the right side of the x-axis in an anti-clockwise direction.

This angle helps specify the vector's orientation relative to the reference axes.

Conclusion Vectors are represented both symbolically and graphically to illustrate their magnitude and direction. Reference axes (x and y) provide a framework for defining the vector's orientation, while the angle θ specifies its direction relative to the x-axis. Understanding this representation is essential for accurately describing vector quantities in physics.

4.Define resultant vector. How vectors are added by heat-to-tail rule? Explain with the help of a suitable example.

Resultant Vector
A resultant vector is a single vector that represents the combined effect of two or more vectors. It has the same effect as all the individual vectors acting together. When we add multiple vectors, the resultant vector gives us the total effect in terms of both magnitude and direction.

Head-to-Tail Rule The head-to-tail rule is a graphical method used to add vectors. It states that to add two or more vectors, redraw their representative lines such that the head of one vector coincides with the tail of the other. The resultant vector is the single vector directed from the tail of the first vector to the head of the last vector.

Illustration of addition of vectors:
Let's take two vectors v1 and v2 having magnitudes of 300 N and 400 N, acting at angles of 30° and 60° with the x-axis. So,

Vector v1 Magnitude = 300 N, Angle = 30° with the x-axis.
Vector v2: Magnitude = 400 N, Angle = 60° with the x-axis.

Graphical Representation Choosing a Scale:
The selected scale is 100 N=1 cm. Therefore, v1 is drawn as 3 cm (300 N) and v2 is drawn as 4 cm (400 N).

Drawing the Vectors Figure 2.4(a) Shows the vectors v1 andv2 are drawn using the head-to-tail rule, maintaining their magnitudes and angles.

Step 1 Draw v1 as a straight line, making an angle of 30° with the x-axis.
Step 2: Draw v2 starting from the head of v1 and making an angle of 60° with the x-axis.

Determination of Resultant Vector Figure 2.4(b) Illustrates the resultant vector formed by connecting the tail of v1 to the head of v2.

Magnitude

The resultant vector is measured as 6.8 cm.

Using the scale (100 N = 1 cm), the magnitude of the resultant v is calculated as:
v=6.8cm×100 N/cm=680N

Direction The direction is measured as an angle of 49° with the x-axis. So, magnitude of resultant vector is 680 N and its direction is angle 49° with x-axis.

5.Define and explain rest and motion with the help of example. Show that rest and motion are relative to observer.

Rest If a body does not change its position with respect to its surrounding, it is said to be at rest.

Example when a motorcyclist is standing still on the road, an observer can compare the motorcyclist's position to nearby objects such as a building, tree, or pole. If the motorcyclist's position does not change with respect to these objects (Figure 2.5-a), then the observer will conclude that the motorcyclist is at rest.

Motion If a body continuously changes its position with respect to its surrounding, it is said to be in motion.

Example In the case of a motorcyclist who starts driving (Figure 2.5-b), an observer will notice that the motorcyclist's position is changing relative to the same surroundings, such as the building, tree, or pole. Therefore, the observer will conclude that the motorcyclist is in motion.

Relativity of Rest and Motion:
The concepts of rest and motion are relative, meaning they depend on the observer's frame of reference. A body can be at rest in one frame of reference and in motion in another.

Example Consider a person standing inside a moving train. To other passengers inside the train, the person appears to be at rest because their position does not change relative to the train's interior. However, an observer standing on the railway platform will see that the same person is in motion because their position changes relative to the stationary platform.

6.Explain different types of motion and give examples. Further explain types of translatory motion.

In our daily life, we observe various types of motion. Generally, these can be categorized into three main types:

i. Translatory Motion ii. Rotatory motion iii. Vibratory motion

i. Translatory Motion
If the motion of a body is such that every particle of the body moves uniformly in the same direction, it is called translatory motion.

Example (i) The motion of a train or a car is translatory motion.
(ii) Riders moving in a ferries wheel.

Types of Translatory Motion Translatory motion can be classified into three subtypes:

(a) Linear motion
If the body moves along a straight line, it is called linear motion.

Example (i) Motion of freely falling body.
(ii) Aeroplane flying straight in air.

(b) Random motion
If the body moves along an irregular path, the motion is called random motion.

Example (i) The motion of bee
(ii) The motion of gas molecules along a zig-zag path.

(c) Circular motion
The motion of a body along a circle is called circular motion.

Example (i) Motion of ball tied to one end of string.
(ii) Motion of moon around the earth.

ii. Rotatory motion:
If each point of a body moves around a fixed point (axis), the motion of this body is called rotatory motion.

Example (i) The motion of an electric fan.
(ii) Motiof drum of a washing machine dryer.
(iii) Motion of top.
(iv) Motion of a cycle wheel.

iii. Vibratory motion:
When a body repeats its to and fro motion about a fixed position, the motion is called vibratory motion.

Example (i) The motion of a swing in a children park.
(ii) Motion of simple pendulum.

7.Differentiate between Distance and Displacement.

Distance Distance is the length of the actual path of motion.

Nature of quantity It is a scalar quantity, meaning it has only magnitude and no direction.

Displacement Displacement is shortest distance between initial and final position.

Nature of quantity The displacement of an object is a vector quantity whose magnitude is the shortest distance between the initial and final positions of the motion and its direction is from the initial position to the final position.

Example Let a person travel from Lahore to Multan in a car (Fig.2.6). On reaching Multan, the person notices on the speedometer that the distance traveled is 320 km. This represents the total path covered by the car, which is the distance. However, this is not the shortest distance between Lahore and Multan, as the car took many turns along the way. The displacement, in this case, would be the shortest straight-line distance from Lahore to Multan, with a direction from Lahore to Multan.

Note Distance is always greater than or equal to the magnitude of displacement.

8.Explain the concepts of speed and velocity. Also discuss uniform and non-uniform velocity with an example.

Speed Speed is defined as the distance covered in unit time.

Formula If S is the distance covered by body in unit time 't', then.

Speed = Distance covered / time taken

i.e. v= S / t or Distance = Speed × time or S = v × t

Speed is a scalar quantity. The SI unit of speed is meters per second (m/s) or kilometers per hour (km/h).

Instantaneous Speed The speed of a vehicle that is shown by its speedometer at any instant is called instantaneous speed.

Average Speed Defined as the total distance divided by the total time taken.

Average Speed = Total Distance covered / total time taken or v_av = S / t

Velocity The net displacement of a body in unit time is called velocity.

velocity = Displacement / time

i.e. v = d / t or d = v × t

Example If a car is moving towards the north at the rate of 70 km/h, the speed of the car is 70 km/h, a scalar quantity. However, the velocity of the car is a vector quantity, with a magnitude of 70 km/h directed towards the north.

Uniform velocity The velocity is said to be uniform if the speed and direction of a moving body does not change.

Non-uniform velocity If the speed or direction or both of them changes, it is known as variable velocity or non-uniform velocity.

Example The example of a body moving with uniform velocity is the downward motion of a paratrooper. When a paratrooper jumps from an aeroplane, he falls freely for a few moments. Then the parachute opens. At this stage the force of gravity acting downwards on the paratrooper is balanced by the resistance of air on the parachute that acts upward. Consequently, the paratrooper moves down with uniform velocity.

9.Explain the concept of acceleration and its types. Also discuss uniform and non-uniform acceleration.

Acceleration Acceleration is defined as the time rate of change of velocity. It occurs when there is a change in the magnitude or direction of velocity, or both.

Types of Acceleration

Positive Acceleration When the velocity of an object increases, it experiences positive acceleration.

Example When a car overtakes another one, it accelerates to a greater velocity.

Negative Acceleration (Deceleration/Retardation) When the velocity of an object decreases, the acceleration is negative.

Example When brakes are applied to slow down a bicycle or a car, it undergoes deceleration

Formula Average acceleration = change in velocity / time taken

a_av = (vf - vi) / t or a_av = Δv / t

The SI unit of acceleration is meters per second square (m/s²).

If acceleration a is constant then above equation can be written as vf = vi + at

Uniform and non-uniform acceleration

Uniform Acceleration If the rate of change of velocity is constant, the acceleration is said to be uniform.

Non-uniform acceleration If anyone of the magnitude or direction or both of them changes it is called variable or non-uniform acceleration.

10.What is a graph? How it is drawn? Explain.

Graphical Analysis of Motion

A graph is a pictorial diagram, represented by a straight line or a curve, that shows the relationship between two physical quantities. It is commonly drawn on graph paper with equally spaced horizontal and vertical lines. The intersection points of the horizontal lines (x-axis) and vertical (y-axis) lines is called the origin (O).

Axes Representation

X-axis (Horizontal) Represents the independent variable, usually time (t). Positive values are plotted to the right, and negative values to the left of the origin.

Y-axis (Vertical) Represents the dependent variable, such as distance (S). Positive values are above the origin, and negative values are below.

11.What is distance-time graph? Explain steps to draw a graph on a paper.

Distance-Time Graph
Distance-time graph shows the relation between distance S and time t taken by a moving body.

Let a car be moving in a straight line on a motorway. Suppose that we measure its distance from starting point after every one minute, and record it in the table given below:

Time t (min) - 0 - 1 - 2 - 3 - 4 - 5
Distance S (km) - 0 - 1.2 - 2.4 - 3.6 - 4.8 - 6.0

Follow the steps given below to draw a graph on a centimetre graph paper:
(i) Take time t along x-axis and distance S along y-axis.
(ii) Select suitable scales (1 minute = 1 cm) along x-axis and (1.2 km = 1 cm) along y-axis. The graph paper shown here is not to the scale.
(iii) Mark the values of each big division along x and y axes according to the scale.
(iv) Plot all pairs of values of time and distance by marking point on the graph paper.
(v) Join all the plotted points to obtain a best straight line as shown in Fig. 2.8. from the table, we can observe that car has covered equal distance in equal intervals of time. This shows that the car moves with uniform speed. Therefore, a straight line graph between time and distance represents motion with uniform speed.

(a) Now consider another journey of the car as recorded in the table given below:

Time t (min) - 0 - 1 - 2 - 3 - 4 - 5
Distance S (km) - 0 - 0.240 - 0.960 - 2.160 - 3.840 - 6.000

Table shows that speed goes on increasing in equal intervals of time. This is very obvious from the graph as shown in Fig. 2.9. The graph line is curved upward. This is the case when the body (car) is moving with certain acceleration.

12.Explain distance time graph for an object: (i) When speed of object decreases (ii) When object is at rest

(i) Distance time graph when speed of an object decreases:

Time t (min) - 0 - 1 - 2 - 3 - 4 - 5
Distance S (km) - 0 - 2.0 - 3.1 - 4.0 - 4.6 - 5.0

The slope of graph is curved downward. This shows that distance travelled in the same interval of time goes on decreasing, so speed is decreasing. This is the case of motion with deceleration or, negative acceleration as shown in Fig. 2.10

(ii) Distance-time graph when object is at rest:

Time t (min) - 0 - 1 - 2 - 3 - 4 - 5
Distance (km) - 1.2 - 1.2 - 1.2 - 1.2 - 1.2 - 1.2

Ans Slope is horizontal in this case (Fig 2.11). It shows that the distance covered by the car does not change with change in time. It means that the car is not moving; it is at rest.

13.Explain gradient of distance-time graph. What does the gradient of distance-time graph represents?

(i) Introduction to Gradient and Distance-Time Graph:

The gradient is the measure of the slope of a line on a graph. For a distance-time graph, this slope represents how distance changes with respect to time, indicating the speed of an object.

(ii) Selecting Points P and Q:

To calculate the gradient, select any two points in time, t1 and t2, on the x-axis. Draw vertical dotted lines from these points to meet the graph at points P and Q. These points represent the positions of the object at times t1 and t2.

(iii) Drawing Horizontal Lines for Distance:

From points P and Q, draw horizontal lines to intersect the y-axis at points S1 and S2. These intersections represent the distances S1 and S2 covered by the object at times t1 and t2, respectively.

(iv) Calculating the Change in Distance and Time:

The distance covered in the interval is given by: S2 - S1 = ΔS
The time taken for this interval is: t2 - t1 = Δt

(v) Determining the Gradient (Slope):

The slope or gradient of the line connecting points P and Q is calculated using:
Slope = RQ / PR
Slope = (change in distance) / (change in time) = (S2 - s1) / (t2 - t1) = ΔS / Δt

(vi) Relationship with Average Speed:

The average speed of the object is: vav = ΔS / Δt

This is the same as the slope of the distance-time graph. Therefore, the gradient of the distance-time graph is equal to the average speed.

(vii) Tangent θ and Graph Line:

The slope of the graph line is also expressed as the tangent of the angle θ formed between the graph line and the time axis: tan θ = ΔS / Δt

Conclusion Gradient of distance-time graph is equal to the average speed of the body.

14.Explain speed-time graph when an object: (i) moving with uniform acceleration (ii) moving with constant speed

Speed Time Graph

Suppose we can note the speed of the same car after everyone second and record it in the table given below, we can draw the graph between speed v versus time t. This is called speed-time graph.

(i) When an object moving with uniform acceleration:

Table
Time t (s) - 0 - 1 - 2 - 3 - 4 - 5
Speed v(ms^-1) - 0 - 8 - 16 - 24 - 32 - 40

Take t along x-axis and v along y-axis. Scale can be selected as 1s = 1 cm (x-axis) and speed 10ms^-1 = 1 cm along y-axis.

Slope of the graph is shown in Fig. 2.13. It is a straight line rising upward. This shows that speed increases by the same amount after every one second. This is a motion with uniform acceleration. It is also evident from the table.

(ii) When an object moving with constant speed:

Now consider another case. The observations are recorded in the table given below:

Time t (s) - 0 - 1 - 2 - 3 - 4 - 5
Speed v(ms^-1) - 20 - 20 - 20 - 20 - 20 - 20

In this case, graph line in horizontal (Fig 2.14) parallel to time x-axis. It shows that speed does not change with change in time. This is a motion with constant speed.

15.Explain gradient of speed-time graph. What does gradient of speed-time represent? Find the gradient of speed-time graph for an object moving with constant speed.

The gradient (or slope) of a speed-time graph provides essential information about the acceleration of a moving object. Depending on the nature of the motion, the slope varies and reflects either a constant acceleration or constant speed.

Let's analyze these two scenarios in detail.

Motion with Constant Acceleration

In this scenario, the speed of an object changes uniformly over time. Consider the speeds at times t1 and t2 as v1 and v2, respectively. The change in speed (Δv) over the time interval (Δt) is expressed as:

Δv = v2 - v1 and Δt = t2 - t1

The gradient (slope) of the speed-time graph is calculated as:

Slope = (change in speed) / (change in time) = (v2 - v1) / (t2 - t1) = Δv / Δt

From the definition of average acceleration (a):

a = Δv / Δt

Hence, the gradient of the speed-time graph equals the average acceleration of the object.

Motion with Constant Speed

When the object's speed does not change with time, it moves with constant speed. In this case, the speeds at times t1 and t2 are the same:

v2 - v1 = 0

Slope = (v2 - v1) / (t2 - t1) = 0 / Δt = 0

This shows that the acceleration of this motion is zero. It is the motion without the change in speed.

16.Show that the area under speed-time graph is numerically equal to the distance covered by an object.

The distance moved by an object can be determined by calculating the area under a speed-time graph.

(i) Distance for Motion with Constant Speed:

When an object moves with a constant speed (v) over a time interval (t), the speed-time graph is a horizontal line at speed v, as shown in Figure 2.17.

The distance covered (s) is given by the equation: S = v × t

The speed-time graph forms a rectangle with Base (t) and Height (v)

The area of the rectangle is given by:
Area = base × height
Area = t × v

Hence, the area under the graph is numerically equal to the distance covered by the object.

(ii) Distance for Motion with Uniformly Increasing Speed:

If the speed of an object increases uniformly from 0 to v over time t, the speed-time graph forms a right-angled triangle (as shown in Figure 2.18).

The average speed (vav) is given by:
vav = (0 + v) / 2 = 1/2 v

The distance covered can then be calculated using the equation:
Distance covered = Average speed × time = (v/2) × t

The speed-time graph forms a triangle, with base (t) and Height (v)

The area of the triangle is given by:
Area = 1/2 × base × height
Area = 1/2 × t × v = (v/2) × t

Hence, the area under the graph equals the distance traveled by the body.

17.Explain the three equations of motion used to solve problem of motion, and what are the assumptions made while applying these equations.

Three equations of motion are used to solve problems for motion of bodies. If vi is the initial velocity of the body, vf is the final velocity, t is the time taken, S is the distance covered and a is the acceleration, then:

vf = vi + at

S = vit + 1/2 at²

2as = vf² - vi²

Assumptions in Applying the Equations:

(i) Motion is always considered along a straight line

(ii) Only the magnitudes of vector quantities are used.

(iii) Acceleration is assumed to be uniform.

(iv) The direction of initial velocity is taken as positive. Other quantities which are in the direction of initial velocity are taken as positive. The quantities in the direction opposite to the initial velocity are taken as negative.

18.Explain the concept of free fall acceleration and describe how the equations of motion are applied to freely falling bodies? What are the important points to consider when using these equations for objects in free fall?

When a body is falling freely under the action of gravity, the acceleration acting on it is called gravitational acceleration, denoted by g. This acceleration always acts downward towards the Earth. The standard value of gravitational acceleration is 9.8 m/s², but for convenience, it is often approximated as 10 m/s².

Since the body moves vertically downward in a straight line with uniform acceleration due to gravity, the three equations of motion can be applied to describe the motion of freely falling bodies. In these equations, the acceleration a is replaced by g, the acceleration due to gravity. The three equations of motion for freely falling bodies are:

vf = vi + gt

S = vit + 1/2 gt²

2gh = vf² - vi²

Important Points to Remember When Using These Equations:

It should be remembered that while using these equations, the following points should be kept in mind:

(i) If a body is released from some height to fall freely, its initial velocity vi will be taken as zero.

(ii) The gravitational acceleration g will be taken as positive in the downward direction. All other quantities will also be taken as positive in the downward direction. The quantities in the direction opposite to the acceleration will be taken as negative.

(iii) If a body is thrown vertically upward, the value of g will be negative and the final velocity will be zero at the highest point.

Unit 2: Kinematics — Long Questions