[Physics Class Notes] on Macro Lens Pdf for Exam

What is Macro Lens?

A Macro lens is a type of camera lens specially used in photography for its ability to capture small subjects at very close distances with much detail, thanks to its much nearer focal length. Ever wondered while looking at a photo of an insect or a flower taken from an extreme closure, what on earth made it possible? All thanks to a macro lens. It takes an ample amount of technical prowess to handle a macro lens; however, it can be addictive when mastered perfectly. The domain of photography that centres on using a macro lens is called Macro Photography, and it has been quite popular since its dawn. It is unlike any other camera lenses; it renders a tiny object with outstanding detail. 

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How Macro Lenses Work?

No need to ponder on the working principle of a macro lens, here we will look into the matter of what goes behind a macro lens using the minimum of technical terms-

The magnification ratio of a macro lens should be 1:1. It means that when the camera is positioned at the closest focusing distance, the image that will be ‘reproduced’ into the sensor will be of the exact size of the subject. For this reason, 1:1 magnification ratio is called ‘life-size’. The focal length of a macro lens is relatively nearer; it stays between 35mm-50mm (more on this later). Thus practically, the magnification ratio of a macro lens stays at 1:2. However, the 1:1 dream mark can be achieved if one uses an extension tube. 

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  • Focal Length – As we mentioned earlier, macro lenses have a nearer focal length. The most popular focal length choice for a macro lens is 90mm-100mm. There is a reason behind this. Stay with me here, the more the focal length of a lens, the more working distance you have between you and your subject. Larger focal length grants you a narrower depth of field so that you can throw the background out of focus a little further. Also, you can snap your shot from a distance. But it comes with a price like literally they are expensive.

In case of lower focal length, you have to be much nearer to your subject to capture your perfect shot. In this process, unwanted things are also prone to happen; for instance, your shadow can get in your way, darkening your field. Insects are prone to fly away if you get closer to them. However, they are much cheaper as well.

That is the reason 90mm-100mm focal length is the most popular that mediates both the quality of your shot and also doesn’t put a hole in your pocket. 

Difference Between Micro And Macro Lens

The topic which we will discuss in this section will address one of the biggest confusions photographers have in the closeup photography realm. However, though they fall under the same category, there is a difference between micro and macro lens. The main difference lies in capturing the most exquisite details. A macro lens captures far better details than a microlens. Some companies name their microlens as a macro lens when they actually are not. A macro lens has the ability to reach the magnification ratio of 1:1. Here we will put two photographs to make things easier for you. The first is taken with a Nikon telephoto lens and the second one is a micro shot. You will notice how the details are much clearer, and the image is more magnified in the second shot. 

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Nikon Telephoto Lens

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Macro Lens

Solved Examples

  1. What is A Macro Lens Used For?

Macro lenses are used to take photos of relatively small subjects, like insects or the intricate patterns of cloth. Macro lenses offer great detail. They are also called life-size for their 1:1 magnification ratio.

  1. What is The Highest Magnification Ratio That Can Be Achieved By A Macro Lens?

The magnification ratio or reproduction ratio that can be achieved by a macro lens is 1:1.

Did You Know

The depth of field of a macro lens can be extremely shallow. Even a millimetre here and there can render your object out of focus. Light is a key factor for macro lenses. More the magnification lesser the light will be in your picture. So it is advised to set up enough light resources when taking a macro shot. Telephoto macro lenses are more expensive than regular macro lenses. 

[Physics Class Notes] on Magnetic Pole Pdf for Exam

A magnet comprises two poles viz: a magnetic north pole and magnetic south pole. A pole that has the strongest magnetic field is the magnetic pole. 

Here, the pole of a magnet is a magnetic monopole, which is a hypothetical elementary particle. 

Suspend a magnet and the place where the magnetic field strength is the strongest is the magnetic pole.

On this page, we will discuss the magnetic field of Earth and the Earth’s magnetic pole with the understanding of the magnetic N-S pole.

What are Magnets?

An object that has the ability to generate a magnetic field around itself is known as a Magnet. A magnet can attract ferrous objects like steel, iron, nickel, and cobalt.

 

History of a Magnet

In the early days, around the period of 600 B.C., the Greeks observed that the naturally occurring element, viz:  ‘lodestone’ attracted iron pieces, and this led a path to the study of magnets. 

In today’s time, magnets are very common as they can even be made artificially (temporary magnets), giving various shapes and sizes.

The best-known example of common magnets that can be seen in our household is the bar magnet. In general terms, a bar magnet is long and rectangular in shape of a uniform cross-section area that attracts pieces of ferrous objects. There are two different poles of a magnet; the magnetic north pole and the magnetic south pole. 

The magnetic compass needle is also a commonly used device that has helped sailors for navigation in the ancient period, and in today’s time as well. 

The needle comprises a small magnet that is free to move horizontally on a fixed point. The two poles of the magnetic compass needle point towards the north and south directions.

The below image shows how a magnet has two poles and the magnetic lines emitting out of the magnet from the magnetic north pole location to the magnetic south pole:

Magnetic North Pole

The north pole of Earth’s magnet is in the poles of Earth. It is a point on the surface of Earth’s Northern Hemisphere at which the magnetic field of Earth vertically points downwards. 

So, if a magnetic compass needle is allowed to rotate around the horizontal axis, it points straight down. 

There is only one magnetic pole location where this occurs, near the Geographic North Pole. The north pole of Earth’s magnet is in the poles of Earth, and it is a related point, is the pole of an ideal dipole model of the magnetic field of Earth that most closely fits the Earth’s actual magnetic field.

Magnetic South Pole

The South Magnetic Pole is the fixed point on the southern hemisphere of the Earth. It is a point where the geomagnetic field lines direct vertically upwards. The Geomagnetic South Pole is a related point or the south pole of an ideal dipole model that most closely fits the Earth’s actual magnetic field.

Earth’s Magnetic Poles

A magnetic pole is a region in which the end of a magnet has the strongest external magnetic field. Magnetic poles of astronomical bodies like the Earth is a special case of magnets, so let’s discuss these:

Magnetic Poles of a Bar Magnet

The bar magnet is an easily available device to visualize the magnetic poles. 

In a bar magnet, the two ends of a permanent magnet are called poles of a magnet or the magnetic poles. The force exerted by a magnet is indicated using curved lines with arrows. 

These magnetic field lines of force along with the magnetic field surrounding the magnet are called magnetic field lines. The arrows on the lines show the direction of a magnetic force, i.e., these lines originate from the North Pole to the South Pole of the magnet.

Now, let’s understand the concept of the magnetic pole in a bar magnet:

When we suspend a bar magnet in the Earth’s magnetic field, it points itself in a north-south direction. 

The north-seeking pole of such a magnet is the magnetic north pole, while the south-seeking pole is called a magnetic south pole. 

We must note that unlike poles of two magnets tend to attract each other while the like poles tend to repel each other.

[Physics Class Notes] on Maximum Power Transfer Theorem Pdf for Exam

In a DC circuit, the source will supply the power to the resistive  load and load receives the power and gets dissipated in the load. We will always try to increase the power transferred to the load by the source. The maximum power transfer theorem deals with the condition when the power supplied by the source is transferred to the resistive load at a maximum rate. We will discuss the maximum power transfer theorem in detail and also solve problems using maximum power transfer theorem.

Maximum Power Transfer Theorem

Maximum power transfer theorem states that the voltage source in a DC circuit  will deliver maximum power to the resistive load connected to the voltage source when the load resistance is equal to the source resistance. We can take a resistive load in a DC circuit which is equal to the resistance of the source and a maximum power will be transferred to the load. By maximum power transfer theorem application, we are able to increase the signal strength in communication systems.

Maximum Power Transfer Theorem Proof

Consider the circuit in which a DC source network is connected to the load resistance as shown in figure A below. We have to find the thevenin voltage and thevenin source of the source and the circuit is transformed to another circuit as shown in figure B.

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To prove the maximum power transfer theorem, we use the circuit shown in figure B. First, we have to find the current passing through the circuit given by,

I = [frac{V_{TH}}{R_{TH}+R_{L}}]…(1)
Where,

I– Current passing through the circuit

V[_{TH}]– Thevenin voltage of the source

R[_{TH}] – Thevenin resistance of the source 

R[_{L}] – Resistance of the load
We can calculate the power delivered to the load resistance by the given equation,

P[_{L}] = I[^{2}]R[_{L}]… (2)   
Where,

P[_{L}] – Power delivered to the load

Now, substitute the value of I from equation (1) in equation (2) to obtain the power delivered to the load resistance in terms of thevenin voltage.


P[_{L}] = I[^{2}]R[_{L}]
P[_{L}] =[left ( frac{V_{TH}}{R_{TH}+R_{L}} right )^{2} R_{L}]…(3)                  

Differentiate the equation with respect to RL and equate to zero to obtain the condition for maximum power transfer

⇒[frac{dP_{L}}{dR_{L}}]=0

[frac{dP_{L}}{dR_{L}}]=[frac{d}{dR_{L}}][left[left(frac{V_{TH}}{R_{TH}+R_{L}} right )^{2} R_{L} right ]]=0

[frac{V^{2}_{TH}left ( R_{TH}-R_{L} right )}{left ( R_{TH}+R_{L} right )^{2}}]=0

(R[_{TH}]-R[_{L}])=0

R[_{TH}] =R[_{L}]

Therefore, the power delivered to the load resistance is maximum when the thevenin resistance is equal to the load resistance. This is in accordance with the maximum power transfer theorem. Hence, the maximum power transfer theorem is proved.

Maximum Power Delivered to Load Resistance

We have seen the maximum power transfer theorem proof. Now, let’s calculate the maximum power delivered to the load resistance when thevenin resistance is equal to the load resistance.

For the maximum power transfer to occur,

R[_{TH}]=R[_{L}]
Substitute R[_{TH}] in the place of R[_{L}] in the equation for power delivered to the load resistance to obtain the maximum power delivered.

Then maximum power delivered to the load resistance is given by,

P[_{max}] =[left ( frac{V_{TH}}{R_{TH}+R_{TH}} right )^{2} R_{TH}]

P[_{max}] = [left ( frac{V_{TH}}{2R_{TH}} right )^{2} R_{TH}]

P[_{max}] = [frac{V^{2}_{TH}}{4R_{TH}}]

The above equation is the maximum power transfer theorem formula to calculate the maximum power delivered to the load. Therefore, we can calculate the maximum power delivered to load by knowing the thevenin voltage and thevenin resistance.

Steps to Solve Network using Maximum Power Transfer Theorem

Let us see the steps to calculate the maximum power transferred to the load for problems  using the maximum transfer theorem which are given below

Step 1: Identify the variable load resistance in the circuit and remove the load resistance.

Step 2: Replace the independent source voltage by a short circuiting the terminals and the independent current source by an open circuit.

Step 3: Find the thevenin resistance of the circuit by calculating the equivalent resistance between the terminals of the open circuited load resistance.

Step 4: Find the thevenin voltage by calculating the voltage across the terminals of the open circuited load resistance and find the maximum power delivered using the maximum power transfer theorem formula. 

Conclusion

Maximum power transfer theorem states that maximum power will be delivered by a DC source to the load resistance when the load resistance and source resistance are equal. So, if the load resistance is a variable resistance, we can vary the resistance of the load until it becomes equal to the source resistance and maximum power will be transferred to the load. For a given circuit, we can find the thevenin resistance of the circuit and the load resistance has to be equal to the thevenin circuit for a maximum power transfer. During maximum power transfer, the efficiency becomes 50%.

[Physics Class Notes] on Mechanics Pdf for Exam

The subject matter of mechanics is a field that requires practical application of knowledge.  The people and the great scientists who have a good knowledge of mechanics have either been great inventors or have changed the world for the better. The students today with the same aspiration to achieve something great in their lives study mechanics. However, the subject is a little complex in nature and does require some greater intervention from the mentors to enable the students to learn about mechanics well.

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Mechanics is a science that deals with the motion of objects under the effect of force. It also deals with the special case when the body stays at rest.

Here, our foremost concern is with the two bodies that exert forces on each other.

For example, the effect of gravity on the planets revolving around the sun, magnetic forces by which iron filings get attracted to the magnet and the electric force under which the two charges get attracted towards each other, and so on.

Mechanics

Mechanics is the area of physics that is concerned with the movement of physical objects.

Forces applied to objects result in displacements, i.e., changes of an object’s position relative to its surroundings.

Mechanics is divided into three following categories:

Statistical Mechanics

The word static in statistical means stable or at rest. So, statistical mechanics deals with the static objects on which the force is applied. Statistical mechanics combines the principles of statistics with both classical and Quantum Physics.

In today’s era, one of the fundamental concepts (pillars) of Modern Physics is statistical mechanics. Statistical mechanics that treats and explains classical thermodynamics is statistical thermodynamics.

Let’s say, there is ‘N’ number of system of particles in thermal equilibrium at absolute temperature T, the energy E is associated with each particle, then the energy for ‘N’ particles will be:

N (E) = g (E) f (E)

Where,

N (E) = total energy of all the particles in a system.

g (E) = Number of state of energy (E) or the statistical weight regarding the energy

We call f (E) the distribution function.

f (E) has two more meanings:   

Statistical mechanics help us determine how macroscopic properties, viz: temperature and pressure are related to macroscopic properties that keep on varying on an average.

As we know classical thermodynamics can only measure and tabulate the quantities (heat capacity) of certain materials; however, statistical mechanics connects these thermodynamic quantities to microscopic behavior.

Classical Mechanics

Classical mechanics deals with the objects in motion under the influence of a force or the equilibrium bodies whose all forces are balanced.

We can think of classical mechanics as the explanation of basic postulates of Isaac Newton mentioned in his book named Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia.

We call these postulates Newton’s laws of motion. These laws help us forecast with great accuracy a wide variety of phenomena ranging from the motion of individual particles to the interactions of highly complicated systems.

The core concepts in classical mechanics are force, mass, and motion. Newton couldn’t define both mass and force. Since then these both have been the subject of much philosophical observation for Newton. However, both of these are best known for their effects.

Applying the first law of motion, we can say that mass is a measure of the tendency of a body to resist changes in its state of motion, while the force accelerates bodies, i.e., when it is applied to the body, it changes the state of motion of the body. The interconnection between these two effects is what we call classical mechanics.

What is Classical Mechanics in Physics?

Classical mechanics is a theory of Physics that takes into aspect the motion of macroscopic objects (objects visible with naked eyes), starting from projectiles to different parts of machinery, and astronomical objects, such as spacecraft, stars, planets, and galaxies.

For objects that are governed by classical mechanics, if the present state is known, we can predict how an object will move in the future (determinism) and how it has moved in the past (reversibility).

Quantum Mechanics

Quantum mechanics is the theory of science that studies the behavior of matter and light on the atomic and subatomic levels.

Quantum mechanics is the fundamental tool that helps to understand the theoretical stage and the electronic structure of chemical compounds and their mechanism, thermodynamics, chemical kinetics, and kinetics of chemical reactions.

Quantum mechanics attempts to describe and look for the properties of molecules and atoms and their constituents, viz: electrons, protons, neutrons, and many other esoteric particles such as quarks & gluons; these attributes involve the interactions of particles (at the microscopic level) with each other and with electromagnetic radiations such as light-rays, X-rays, and gamma-rays.

So, you understood how quantum physics explains how atoms work, and therefore, why chemistry and biology work as they do.

Points to Remember

Do you know mechanics and kinematics are related to each other? If you don’t know, let’s understand it.

The part of mechanics that describes motion without concerning its causes is called kinematics. It’s because kinematics does not take into account the cause of motion, it only considers the following parameters of motion; these are:

  • Speed   

  • Displacement

  • Distance

  • Time

  • Velocity

Benefits of – Mechanics Article

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[Physics Class Notes] on Mobility Pdf for Exam

Mobility can be defined defined in different ways but in physics when we talk about a solid state the measurement of the ease with which any particular type of charged particle moves through a solid material when that material is under the influence of an electric charge then we can state that mobility has taken place between the charge particle and the electric field. When these particles are pulled along by the electric field they are bound to collide with atoms of the solid. Now with this occurring phenomena we can derive the definition of drift velocity which occurs when a combination of electric field and collision causes the particles to move with an average velocity. We also see that the charge carrier in most metals contains negatively charged electrons.

Now with the drift velocity we can define mobility as the value of the drift velocity per unit of electric field strength so the faster the particle moves at a given electric field strength the larger its mobility will be, mobility may vary with temperature depending on any particular type in any particular solid. The dependence of mobility on the type of solid can be explained by the examples of semiconductors where the electric current is also carried by the motion of positively charged particles namely holes and each of which corresponds to the absence of an electron now with this the condition arises complications of their separate mobilities because there are several electronic devices which require him abilities for officiant operation, we will not look into this at the moment because we will have to enter quantum electro dynamics for that so we will just keep it till mobility and how it depends on the type of solid and other basic characteristics.

We define Mobility in Physics (solid-state Physics) as the measurement of the ease with which charged particles move through a solid material under the influence of an applied electric field.

If we observe the working of an electric circuit when a potential difference is applied across the circuit, electrons get a push and they start mobilizing from one end to the other, and electricity generates, which is how we define mobility of charge carriers like electrons.

On this page, we will understand what is mobility, the unit of mobility, what the relation between mobility and drift velocity is, and the mobility definition in Physics in detail.

 

Electron Scattering

Electron scattering occurs when there is a deflection of the path of electrons when the password is solid, a metal, semi conductor or an insulator. When these electrostatic forces operate between the negatively charged electrons and atoms within the solid, then deflections or collisions are caused. These forces in turn reduce the speed of the electrons by limiting their performance on the electronic devices that we use, based on transistors and integrated circuits. Electron scattering can also be explained by the deflection of a beam of electrons by target, which is also used to prove the size and charge distribution of atomic nuclei. When we talk about electrons and how they scatter we go way back to the 1970s and because of the foundation of electron scattering during that time, it has been proved and has helped us to confirm that protons and neutrons are made up of elementary subatomic particles known as quarks.

 

Electron Paramagnetic Resonance

Electron pair a magnetic resonance under bracket EPR which can also be called as electron spin resonance or a set of selective absorption of weak radio frequency electromagnetic radiation, this phenomena and can be sighted in the microwave region so what basically happens is that the unpaired electrons in the atomic structure of any given material which is simultaneously subjected to a constant strong magnetic field, now with the unpaid electrons and the way they Spain they tend to behave like tiny magnets so when materials that contain such electrons are subjected to a strong stationary magnetic field, the magnetic axis of the unpaid electrons or as we mentioned earlier the elementary magnets, they partially align themselves with the strong external field and deep recess in the field as much as they access of spinning tops often trace concept surfaces similarly as the process in the gravitational field of earth.

When we observe the absorption of energy from the weak alternating magnetic field of the microwave when it’s given frequency corresponds to the natural frequency of the process of the elementary magnets then we define resonance. The measurement of the radiation absorbed works as a function of the changing variable which gives us an electronic paramagnetic resonance spectrum, such a typically graph of microwave energy absorption when compared with applied stationary magnetic field can be used to identify paramagnetic substances with which we can investigate the nature of chemical bonds present within the molecules by identifying the unpaid electrons present and their interaction with the immediate surroundings.

 

Define Mobility in Physics

Under the definition of mobility of charge carriers, we will understand what is electron mobility followed by what is ionic mobility. 

 

Electron Mobility

Now, we will define the mobility of a charge carrier in detail:

In solid-state physics, electron mobility describes how fast an electron can move through a metal or a semiconductor (for mobility in a semiconductor) when charges are pulled by an electric field. 

There is an analogous term for the mobility of holes, called hole mobility. The term carrier mobility is common to both electron mobility and hole mobility.

Electron and hole mobility are out-of-the-box cases of electrical mobility of charged particles in a fluid under the effect of the external electric field.

When an external electric field E is applied across a material, the electrons respond by making a motion with an average velocity called the drift velocity, which is denoted by [V_{d}]. The mobility is denoted by [mu].

The relation between mobility and drift velocity is given by the following equation:

              [V_{d} =  mu E]…..(1)

Equation (1) is the relation between mobility and drift velocity.

[rightarrow mu = frac{V_{d}}{E} ]….(2)

Equation (2) is electron mobility in terms of Mathematics. 

From equation (2), we define mobility of a charge carrier as the value of the drift velocity per unit of electric field strength.

Now, let’s determine the unit of mobility:

 

Unit of Mobility

Electron mobility is always specified in units of [frac{cm^{2}}{(V⋅s)}]. This unit is different from the SI unit of mobility, where the unit of mobility is [frac{m^{2}}{(V⋅s)}]. 

Electron mobility and mobility are related to each other by;

[frac{1 m^{2}}{(V.s)} = frac{10^{4} cm^{2}}{(V⋅s)} ]

 

Mobility in Semiconductor

Mobility in a semiconductor is defined as how speedily charge carriers like electrons move in a semiconductor.

Semiconductor mobility relies on the impurity concentrations in a doped semiconductor that includes the concentrati
ons of both donor and acceptor, defect concentration, temperature, and electron-hole concentrations.

 

Semiconductor Mobility

The logic behind the conductivity in a semiconductor can be understood in terms of electron-hole pairs. 

In the presence of an applied electric field, the electrons and holes move in opposite directions to each other to produce a current. The electric current across a semiconductor is proportional to the voltage applied at its ends.

So, [V = mu E ].  [mu] is called the mobility in semiconductors.

 

Point To Note:

Electron mobility is always greater than hole mobility.

 

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From this graph, we can see that the faster the particle moves at a given electric field strength, the larger the mobility, and vice-versa. 

Also, the mobility of a particular type of particle in a given solid varies with temperature as shown in the above graph.

 

What is Ionic Mobility?

The average velocity or the drift velocity with which an ion drifts through a specified gas under the influence of an electric field is called ionic mobility. 

In simple terms, Ionic Mobility is characterized as the speed achieved by an ion moving through a gas under an applied unit electric field. It is denoted by a symbol  [mu].

 

SI Unit of Ionic Mobility

The unit of ionic mobility is [m^{2}s^{-1} volt^{-1}].

 

Ionic Mobility Calculator

Ionic Mobility calculated by using the following formula:

[text{Ionic Mobility} = frac{text{Speed of Ions}}{text{Potential Gradient}}]

 

Factors Affecting Ionic Mobility

Factors that affect ionic mobility are as follows:

  • Temperature, 

  • Nature of electrolyte, and 

  • Size of an ion

  • The relation between ionic mobility and transportation number is given as;

       [lambda _{a}] or [lambda _{c}] is equal to  [t_{a}] or [t_{c} times lambda _{infty}] 

           Where,

[ lambda _{a}] and [ lambda _{c}], both are ionic mobilities, and

 [t_{a}] or [t_{c}]  = transportation number

  • The ionic mobility is strongly affected by the solvent viscosity and the degree of solvation. The dissociation constants of ions rely on the dielectric constant of the solvent. Therefore, the use of a nonaqueous solvent or the mixed solvent affects the mobility and may improve the separation, viz: the solvent effect. 

 

What is Mobility in Physics?

We know that mobility in Physics is the motion of electrons or ions under the influence of an applied external electric field.

When an electric field is passed, a particular type of charged particle moves through a solid material under the effect of an electric field. 

Such particles are both carried along with the electric field and simultaneously collide with atoms of the solid. 

The combination of electric field and collisions/hitting causes these charge carriers to move with an average velocity, called the drift velocity. The charge carrier in most metals is the negatively charged electron, which is also known as electron scattering. So, now we understand what mobility is.

[Physics Class Notes] on Motion in a Straight Line Pdf for Exam

In Physics, when the position of an object changes over a period of time is known as Motion. Mathematically the Motion is described in terms of displacement, distance, velocity, speed, acceleration, and time. By attaching the frame of reference, the Motion of a body is observed. Further, based on the change in position of the body relative to the frame, the Motion is measured. 

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What is Motion in a Straight Line?

The main aspects of Motion in a Straight Line is discussed in this course by including the difference between the distance and displacement, average velocity and speed, Acceleration along with the exercise of discussion.  Further, solving the problem will grant students a holistic idea about the mechanics of Motion in a Straight Line.

The student should accumulate the knowledge and skills through this designed course. In each section, various ideas are explained in a simplified manner for the understanding of the student. 

 

Types of Linear Motion

The two types of Linear Motion can be stated as follows:

  1. Uniform Linear Motion

  2. Non-Uniform Linear Motion

A body is known to be in uniform Motion if it covers equal distance in an equal Motion time-span. Here, the Motion is with zero Acceleration and constant velocity.

Whereas, a body is known as non-uniform if it covers an unequal distance in an equal period. It comprises non-zero Acceleration and variable velocity

 

Equations of Motion along a Straight Line

Calculus is the best way to derive the equation governing the Motion in a Straight Line. If the value of the three relations velocity-time, distance-time, and Acceleration-time is known in the mathematical form, the value of the others can be obtained by differentiation or integration

Since

[frac{d}{dt}] (distance) = velocity (v)

and

[frac{v}{vt}] (velocity) = Acceleration (a)

There is another method known as the graphical method, which can be used if a precise mathematical relation cannot be obtained. The below figure shows the graphical representation Motion of a horse during a race and how the significant features of each graph are related to others.

 

Motion in a Straight Line Formulas

Constant Acceleration

This segment should be entitled “One-dimensional equations of Motion for constant Acceleration” for the sake of precision, as it will be a nightmare for a stylistic till let me begin this section with the following relations.

Velocity-time

During a uniform Acceleration, the Line of Motion is Straight; the longer the Acceleration greater will be the change in velocity. Hence the relation between velocity and time will be simple during the uniform Acceleration.

a= ∆v / ∆t

Enlarge ∆v to v − v₀ and condense ∆t to t.

a= (v−v₀) / t

Then resolve for v as a function of t.

v = v₀ + at 

The second equation of Motion is written like a polynomial – a constant term (s0), followed by a first-order term (v0t) and followed by a second-order term (½at2). Since the maximum order is 2, it’s more accurate to call it a quadratic.

∆s = v₀t + ½at² 

The third equation of Motion – In this once again, the symbol s0 is the initial stance, and s is the position some time t later. If you prefer, you may pen the equation using ∆s — the change in stance, displacement, or distance as the situation merits.

v² = v₀² + 2a∆s 

Indeed, a quick solution, it wasn’t that difficult compared to the first two derivations. It, however, worked because Acceleration was constant in time and space.

Below are the formulas of Motion in a Straight Line:

v =u + at

s=ut+1/2at²

v² = u² + 2as

Linear Motion Definition

A one-dimensional gesture along a Straight Line and which can be described by using only one longitudinal dimension is known as Linear Motion or rectiLinear Motion. The Linear Motion is divided into two types: one is uniform Linear Motion with constant velocity or zero Acceleration, and the second one is non-uniform Linear Motion with a variety of velocity or non-zero Acceleration. The movement of a particle along the Line can be described by its position, which varies with time. For example, an athlete running 100m along a Straight track is known as Linear Motion.

It is one of the most basic Motions. As per Newton’s first law of Motion, any object that doesn’t feel any net force will continue to go in a Straight Line with a perpetual velocity until it is subjected to a net force. In everyday circumstances, external forces such as friction and gravity can cause a change in the direction of its Motion; hence its Motion cannot be described as Linear.  

Important Questions for Motion in a Straight Line

Here are a few questions from the topic Motion in a Straight Line that will help the students to prepare well from the perspective of the final exams.

  1. Out of the following examples of Motion, which of the body can be considered approximately a point object:

  1. A tumbling beaker which is slipped off the edge of a table

  2. A monkey sitting on the top of a smoothly cycling man who is on a circular track.

  3. A railway carriage moving between two stations without jerks. 

  4. A spin ball of cricket that turns sharply on hitting the ground

  1. The position-time (denoted by x-t) graphs for two children namely ‘A’ and ‘B’ who are returning from their school O to their homes P and Q respectively. Choose the correct answers in the brackets as follows;

  1. (A/B) lives near to the school than (B/A)

  2. (A/B) overtakes (B/A) on the road to school (once/twice)

  3. (A/B) walks faster than (B/A)

  4. A and B both reach their home at the (same/different) time

  5. (A/B) starts walking from the school earlier than (B/A)