Electric flux

Yesterday I watched some of the videos of Walter Lewin lectures on Electricity and Magnetism. He is really amazing especially when he is doing experiments. Thought the concepts are a familiar one it gave me a good time pass. I spend a little time on thinking about Electrostatics.

We need to know that Electric field lines are not real. It is just a simple representation invented by Michael Faraday to visualize Electric field. We should not simply accept it as the real fact.

Electric flux is the measure of the number of field lines passing through the surface that is chosen. But it is not the number of the absolute number of field lines.

The electric flux “ϕ” over a surface S is therefore given by the surface integral:

ϕ = ∬ E. ds

       s

where “E” is the electric field and “ds” is a differential area on the surface S with the normally outward facing direction.

And the electric flux around the closed surface “S” is given by:

ϕ = ∯ E. ds = q / ϵ

But be careful that it is not absolute that, there is exactly 

“q / ϵ” electric flux around a point charge “q” [In SI unit system].

Electric flux is not really the measurement of the number of field lines around a charge. It is just a calculating tool of Electric strength on the basis of proportionality arguments.

We know that we can draw infinitely many electric field lines as much as we want. But for the sake of simplicity in our calculations, we can’t use “infinite” as a number.

[Note: We need to be very careful that “∞” is not a number. It is just a symbol given for concepts.

It is like instead of saying “Newton’s Laws of Motion”, if I made a code “£” in a book, it says that where ever I use the symbol “£” it really means “Newton’s laws of Motion”.

In the same manner, the symbol “∞” is also used just to represent a Mathematical and Physical concept. The “∞” symbol just says that “it gets bigger and bigger where there is no end”. Simply it means “no limit or end”.]  

So we made a proportionality factor that is related with the number of field lines. Though the number of lines is infinite it is a proportional and dependent quantity.  

It was defined the Electric flux as it is proportional to the number of field lines.

It is already known from the definition that charge “q” is also proportional to the number of field lines.

Therefore we made calculations from the conclusion; Electric flux is proportional to “q”

It is first formulated by Carl Freidrich Gauss that is

The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.

If the number of field lines was found out to be increasing that implies the charge “q” inside the closed surface is increased.

In SI units the proportionality constant is taken to be “1/ϵ” and so the electric flux  

Thus we are just finding the proportional increase in Electric flux from “q/ϵ” but it is not the measure of the absolute electric flux around the space of the charge “q”. 

Shadows of the Mind

In these days I have been reading two books. The first one is, “The Shadows of the Mind” by Roger Penrose. Second is “Classical Dynamics of Particles and Systems” by Jerry B. Marion.

First I want to share about the Shadows of the Mind.

Though that book is little vague and complicated for me to understand, I enjoyed it reading. I learned some new concepts in physics and some new way of thinking.

First of all I am very much impressed with the beginning of the book where it was told about a little story of a daughter asking ingenious questions to his father. No matter about the names of the people. But it reminded me about my old time where my teacher used to tell me about our minds.

One day I went straight to my teacher and asked some questions, which later I came to know that they are the basic philosophical questions.  But they are simple questions like,

“Where are we? What is the end of the world? Where is the Universe? If Universe is there somewhere then where that place is situated? What is time? What really we are doing here in this Universe?”

These are the questions often comes to my mind and make me to think I am in the middle of a great mystery.

Really we are all in the middle of the very great mysterious and magical world ‼!

After asking these questions, my teacher said,

“Think that, there are fishes living very deep down in Atlantic or Pacific or any other ocean. It is very deep that is its depth is comparable to height of Mount Everest. The fish spends its whole time in the sea below that depth.

Now, if you and go one day and ask the fish “What is Air? What is Sun, moon and What is Space?”

Do you think it will know the answers?

To that fish the ocean is the only world. In other words, it will think the whole world is completely just filled with water. It will only know about the things that behave in the ocean.

But it never knows about air, sun, moon or space. It even can’t simply imagine the things outside the ocean.”

And he finally said that we are also just like those fishes and where else Scientists are like special kind of fishes, which tries to get out from that ocean.     

It is same as the story told in the preface of the book “Shadows of the Mind”. It is true that we can’t even imagine the world outside the Universe.

When you read these kinds of books, and when you understood a little, stop reading and try to think something more about us. Think about the place of humans in this Universe and Just wonder the universe.

From that book I learned some new basic outline of Quantum Mechanics. Though I couldn’t fully understand Elitzur Vaidman bomb testing problem and Magical Dodecahedra problem, I just had some outline of those concepts.

I learned about Turing machine, Church’s thesis, Gödel’s theorem.

Especially I learned a little about the concept of Spin in sub atomic particles which is not the spin we really imagine in real life.

Spin:

The subatomic spin is somewhat different from classical spin where the axis is fixed in one direction. Unlike classical quantum spin is directed in all directions and “h bar” is the unit by which spin is measured.

In quantum mechanical spin, 

first we will chose a direction in space and using Stern-Gerlach instrument we will just find the magnitude of spin in that direction in space. “h bar” is the unit to denote the magnitude of the spin in that direction.

I learned new things about PULSARs and about PSR 1913-16 that is Hulse Taylor Binary Pulsar. I learned how it was proved General Theory of Relativity by the predictions made in Binary Star System and how it was predicted gravitational waves. I learned what is meant by Gravitational lensing.

Though already I know some of the things, the books gave me a lot of information.   

Basic Outline of Relativity

We can understand the basic outline of theory of relativity in a simple following way from Fermat’s principle of least time.

First you need to understand Fermat’s Principle of least time.

It states that the path taken between two points by “a ray of light” is the path that can be traversed in the least time. So it implies light will always travel in the shortest path between two points.

After believing in this principle, we can take an example of moving rocket with 9.8 m/s^2 of acceleration and earth.

From Newton’s Gravitational law, it was known that all objects near to the earth will fall at a rate of acceleration 9.8 m/s^2. Many of them had learnt this in their school days. Consider that the rocket is at first on earth at rest. If you are inside the rocket, you will see the things inside the rocket will fall at a rate of 9.8 m/s^2 when it is subjected to fall from a height not comparable to the radius of the earth.

[Since gravitational field of earth will be different at different places]

Now, I made you to sleep in the rocket by giving you anesthesia. After you had slept, the rocket was started and made to fly into the space with an acceleration of 9.8 m/s^2 .

From Newton’s law it is known that a man inside the rocket will not feel any difference between these two situations. So, he will think he is still at earth, since the experiments done in the rocket will be as same as it is at earth.

Now if you take torch light and pointed it on the horizontal direction, from very careful measurements you can see that light beam bends exactly same amount as it is in earth.

Since all the experiments done with other objects gives same results in earth as well as in rocket, it implies Light should also give same results independent of the place. 

Thus we came to know that Light indeed bend near the gravitational field. 

From this we can get two information.

One is,

• Newton’s Gravitational law says that only masses are attracted by gravitational force. But here light is attracted towards the earth, where light is thought to be pure energy. It shows that energy and mass has some relation.

The second information is derived from Fermat’s principle.

• If light travels in the shortest path between two points,

In horizontal direction the shortest path between the two points is the straight line drawn between those two points. But light here is actually travels in a bend path not following Fermat’s principle.

To make Fermat’s principle the true one, it was just made a small adjustment in the statement that follows as,

The shortest path between the two points in horizontal direction near the gravitational field is really the bend path.

That says that the space itself is a curved one. And light travels in the shortest path in that curved space where the path of the light is curved. Thus we can get two aspects of Relativity theory.

I am explaining here just the simple outline of Relativity theory and not the complete one.

This is to get just a little basic knowledge of Relativity theory to common people.  

Understanding Newton's Third Law

Though everyone learned Newton’s Third Law in elementary school level, I had seen many of the people doing this mistake while understanding it. I am not an exception at my school level.
The mistake is this,
If I ask a school student to identify all the action and reaction pairs in the photo of an apple that is on a table,

The student will immediately give the answer as only one pair and that is ,
Action: Earth pulls apple with the Gravitational force acting downwards direction [direction towards the earth].
Reaction: Table pushes apple with the Normal reaction acting upwards that is opposite to the direction towards the earth.
The student forgets to realize the fact, since his mind is fully concentrated only on the word Opposite.
But here is what you have to note or surprise about the ingeniousness of Newton. He didn’t had done the mistake as same as the student did.
Before proposing the Third law, Newton cleverly thought about another experiment that is a falling apple towards the earth. It is the perfect example where one can really understand the Newton’s Third Law.

While considering the case of a falling apple and trying to identify the action and the reaction pairs,

Some of the photos of falling apple are as follows,

From his gravitational law, he was known that some force of attraction is there between an apple and the Earth.
Mostly in our first thought we will only realize the Action,
Action: Earth pulls Apple with gravitational force acting downwards that is to the Centre of Mass of the Earth.
But the amazing fact lies there in its pair,
From the relative frame of reference and from the gravitational law, it should be there the reaction as,
Reaction: Apple pulls Earth with same gravitational force acting upward toward the Centre of mass of Apple.  
Note:  It needn’t be earth pulls apple should be action or Apple pulls Earth should be action. Either one of the force can be action or reaction since action, reaction happens simultaneously.
Note: Both these force pairs are same in magnitude. The forces are same but not the acceleration. Acceleration of Earth is so minute and the acceleration of Apple is so high that is 9.8 m/s^2 near to the ground.

On hearing this first time, I take time to believe this fact in my childhood. I thought, How can this small apple pull The Whole Earth upwards? It looked crazy to me.
But then I realized the fact. Since the Mass of the Earth is too large the acceleration of the Earth is so minute so that it couldn’t be seen with our eyes. Nevertheless it is a wonderful and amazing fact that everyone should know.
These kind of mistakes are often in our everyday lives. Thank God for the sake of Newton never did the Same mistake.
The real action, reaction pairs are explained by Newton as follows, 
For every force there is an equivalent and opposite force acting on the opposite direction of the force. You cannot say which force is action and which is reaction. Action and reaction happens at same time. The forces are same in magnitude and Opposite in direction.
Moreover everyone need to note this special point that is,
Note: The action and reaction pair should always be the Same Kind of Force.
That is for an action of gravitational force the reaction force cannot be the Normal force or any other force. It should be also the same Gravitational force.
And that is the note where most of the Students are getting wrong. Do this mistake as I did in your school age because when you did find the real answer you will be amazed like me.
Why I am explaining this mistake is because it is the first thing that made me very much interested in Physics. From this, I started to see the Physics as a Magical one that explains all the Magic in this great enormous Universe.

Answer to the first question (If you need):

Contradiction of Symmetry - 2

Thinking about the Symmetry Contradiction, I understood that the initial conditions are not the same since the inputs smell, sound, visuals are different and they affect the chemical process in our mind and so they will behave like different chemical process.

That is the 5 senses makes us to think different.

Though then, I thought again the same experiment in empty space, where there is no sound, smell, taste (chemical effects), touching (external effect on our skin), and light (being the empty space). Now will they think the exactly in a same way?

I think they will not, because if they think exactly in a same way, then each of the person (experiment) should walk or do the same. That is, if the first person took his left leg forwards to walk, then the it implies that the second person should also take his left leg to walk [being the same chemical reaction in both the Space due to Symmetry Principle].

But will they take the same left leg ?

I don't think it is a must for both of them to start walking by their same left leg, though they think the same in their minds. They can choose left or right leg. They can also choose to stay in the same place instead of walking. So what happens to Symmetry?

We should consider not only thinking process, but both mental and physical process. Physical process also should be the same for both of the person, if Symmetry works in Nature.

I think the reason is something due to Space. Space has something to do with the Symmetries in Nature. But somehow it is not affecting the usual chemical process we are encountering in our everyday lives. The space interacts with the symmetry in Nature. We should work further in this Contradiction to get the idea of what is happening here.

May be the solution for this Contradiction will give us the answer to the formation of life in humans. Moreover it gives more insight to soul or what is meant by spirituality in humans. It will lead to some great conclusion. We should give some importance in a mathematical way to this Contradiction to get the solution.

Power Macintosh 9500/150

           I have an apple computer that is aged more than 15 years. This model is released by May 1 , 1995. It is Power Macintosh 9500/150.
Today I just opened it to look the components and structure of that computer. 
          This Macintosh Computer is quite different from the modern computers. I just took some photos of that computer. Since I am just starting to know about the history and the evolution of computers, this is the first old computer I investigated though I have modern windows computers. 
          Some of the photos of Power Macintosh 9500/150,                                      

                                       Front view

Side views

Peripheral Component Interconnect Card

(PCI Card)

Pascaline - Pascal's Calculator

The evolution of Computers starts with the inventions of Mechanical Calculators and Electronic Calculators. Only from the Inventions of Mechanical and Electronic Calculators, we came to know that Mechanics, and Electronics can also be used to do calculation works other than muscle works done by humans. 

            These Calculators are the basic and fundamental seed for our modern computers. In that way first we need to know about some basic 

          The pascaline works on the basis of gear mechanism. Only Natural numbers are used in pascaline. Only Addition, Subtraction could be done using this calculator.   
         It is the first idea that is based on a mechanical calculation.
A rotating wheel with 10 spokes is attached with a continuous of wheels. It is arranged in such a way that when a wheel rotates one full rotation, a spoke in the neighbourhood that is left to the corresponding wheel will turn up to one spoke.

To do addition, we will just put the desired value by rotating the wheel spokes to desired values. The 10 spokes in a wheel serves as the 10 digits in number system. The number of wheels represents the number of decimal places in a number. 

The wheel can be rotated only in one direction. There will be two lines to represent the initial values of decimal values that is value 1, 2. So that we can understand how to rotate the wheel to get other values. Mostly the wheels are used to rotate clock wise direction. 


I think this link will help you more to understand about Pascaline,

http://www.youtube.com/watch?v=3h71HAJWnVU

Contradiction of Symmetry

When I was thinking about the symmetry in nature, I ended with a contradiction.

First of all what I meant by symmetry is the symmetry in nature. It is that if you do an experiment at your house and if you do the same experiment at your school with same initial conditions, then it will give you the same result.  The experiment can be either physics or chemistry.

For example, if you throw a ball with an initial velocity with some initial conditions it will attain some final velocity. With same initial conditions if you throw the same ball with same initial velocity, from the equations of motion the ball will attain the same final velocity. No matter whether this experiment is done at India or U.S.A or China or Russia, the experiment will give same result. The rule is just the initial conditions should be kept the same.

            Similar kind of example can be given in chemistry.

A chemical process at certain temperature, pressure and other state variables at some value will give same result if the experiment is done with same initial conditions anywhere in the Universe.

Simply it can be said that,

          
          Any process with same initial conditions will give same result independent of place or time. That is any process is symmetrical about space and time.

This symmetry is the base of our entire Science knowledge. If the universe doesn’t follow this symmetry principle, our world would be a big confusion.

The symmetry principle just states that,

         “The Universe that is the Nature follows some specific rules”.

          And Physics is nothing but the study of these rules of the Universe.

But there is contradiction, when you apply this theory in Biology. As per the Science of Biology, human body can be considered as the combination of DNA, RNA and other things. Basically speaking,

Human body is simply the different combination of molecules in Nature. The whole body can be divided into molecules and atoms.

If it could be considered that human body can be created from these tiny molecules, which is like a building created by stones, bricks, rods, cement then the whole of the human body could be built just with molecules.

Let us say it was found a machine to make desired molecules with atoms and that machine can build any structure of any set of molecules in Nature [like building things in Lego game - shown below]. Then it is possible to build human body as a building construction from top to bottom or centre part to side parts. And also let us say all these things are done with same initial conditions as it were build inside a woman’s womb.

Thus let us assume that we able to build two humans with all molecules and atoms at same positions.

Why I need to build these two because clones also may have small differences in their structure. Though DNA, RNA and other things be the same, it would not be exact same. Some small molecules may be in different positions.

But here it was assumed that the two humans build with this machine are exactly the same. That is like an exact printed copy.  

I called the two humans as two experiments. Since both humans are exactly the same, both are same experiments with same initial conditions.

Now I put these two experiments [two humans] at different places of the world.

[Notice that the initial conditions are exactly the same as they were the exact clones and it is fair to say the two humans as experiment because they are nothing but just the mixture of chemical compounds of tiny molecules. Both have same Genes and everything the same.]

Since their initial conditions are all same, they should think exactly the same. But it will not happen at all.

If the first one [first experiment] was put in a market full of crowds, he will start to think about that crowds and may fear about the people and will think who they are.

[These two are like newly born children. They don’t have anything stored in their mind. Their minds are purely fresh and non-polluted.]

And if the second one [second experiment] was put in a room with no people, he will start to think about that whole place and will start to fear where he is. He will be somewhat amused and feared.

This is the contradiction I end up with.

Both are the exactly the same experiment with same initial conditions but had been put on different places in space and time. They didn’t think exactly in a same way. The outside world affected the symmetry principle.
This may happen if they two were brought up in empty space also. 

Somewhat it makes me confusing.

And this is what I want to finally convey,

Whether Symmetry really exists in nature?  
Please give your opinions about this contradiction. 

Stage of Death

I read this story in a book ,

Once there is a man who is crying for the death of his beloved one.

A saint showed up there on his way back to his place. He saw the man crying in his house thinking about the dead past.

            The saint went to him and asked about the reason. And the saint looked through the house and took an old photo of that man taken in his childhood.

            He did see it for a while and asked the man,

“ Where is this young man now?”

The man replied, “ It is me”

The saint asked again the same question, “Where is this young man now?”

The man get confused and replied, “ It is me. I am here. ”

The saint asked exactly the same question again for the third time. This time the man get fully confused and stood silent.

Now the saint advised him saying,

“ Oh child! The young man here at this photo is dead by now. When you grow up that is when you reached a new stage, the past stage of your life becomes dead.

In the same way, from death your beloved one reached a new stage of the life.

From death everyone attains a new stage of our life.

So don’t be worried about death. It is not the end of our life.”

From this story, I really amazed at the words of that saint. It is really true that when we attain a new stage of our life, our past stage gets dead.

Simple but meaningful words

Give a little time to those words.

Small to Big

In these days I have been thinking about the difference between the quantum and classical mechanics. Why these two things need completely different type of thinking?

How does the Universe know to act different in different situations. Same universe in microscope world acts completely different from macroscopic world.
 How it can be possible to the Nature to realize that it is at microscopic level.  
 It is like Nature has a brain or a machine that behaves with some rules. 
Simply if you think nature as a human, then he acts as  person - 1 when he is in macroscopic world and he acts as person -2 in microscopic world. 
Doesn't it look weird about the nature?

If it is so, maybe then we don't know whether Nature behaves as same in the entire universe. 
Maybe in ultra macroscopic level that is at a size of universe, Nature may behave as completely different from the world we are known. It may act as person - 3. 

These things made me confuse about physics whether we are dealing with the real physics of Nature.

Two types of notions arise in my mind.

One is that whether the Nature behaves as same in everywhere around us and whether our theories are somewhat not eligible to explain it.

Second is if Nature behaves different at different levels then maybe it will act completely different in everywhere. And if it is true that it acts as different at different places then 


Why should an atom of hydrogen or any other element that is anywhere in this universe should behave exactly as same as an atom of hydrogen or any other element that is here at Earth. What is the reason for these Symmetrical things in Nature. 

Wikipedia in your hands

Today I was discussing about Maxwell with my friends. In our discussion we came to a doubt that where he was born. We had internet access and so immediately going to the site Wikipedia we got the answer as Scotland.

When you want any information through online you will instantly go to the site Wikipedia.

Wikipedia is the place you can get information about anything and everything

But you can't always have internet access or any broadband services in your latest android mobiles or iphones or in your computer.

Sometimes you will need some important information or you will need to clarify any of your doubts when you don't have internet access.

In those kind of situations, you don't have to go to anywhere else but you can get all the information simply using the software called kiwix in your mobile phones or computers.

Kiwix is an offline reader for web content. It's a software especially intended to make Wikipedia available without using Internet, but it is potentially suitable for all HTML contents.


Full text search engine

Bookmarks & Notes

HTTP server

PDF/HTML export

User interface in more than 100 languages

Tabs navigation

Integrated content manager


Kiwix is a pretty small and efficient software. You can perfectly use it with small or old computers.

It runs on a big range of operating systems, on Android and

on the three main PC operating systems:

To download Kiwix go to this link

You can get any information on Wikipedia using the software kiwix without any type of internet access.

Kiwix is a free software and it is mostly installed in schools, universities and libraries which can't afford a broadband Internet access. It's so much faster than the Internet and also can be used by many institutions to save bandwidth and reader's time.

Kiwix is really easy to use. It provides a range of features which make the usage comfortable:

Microsoft Windows,

Apple Mac OSX and

GNU/Linux distributions.

http://www.kiwix.org/wiki/Main_Page

How to Download from torrentz

There are a lots of science and other resources you can download it from torrent. 

I struggled a little at the starting on How to download books, videos, music and movies using torrent. But then I learnt it quickly.

      For the people who want to download using torrent, please follow these steps

First You need to download a Bit Torrent client, so it speaks the Bit Torrent protocol, much like a browser would speak HTTP.

µTorrent is the most popular bit torrent client. Torch web browser is also one of the most popular bit torrent client.

To download µTorrent click on this below link

http://www.utorrent.com/downloads/win

(or) in your search engine search “utorrent free download” then download the software you want.

The setup file will be downloaded in your computer.

Now open the setup file and run it on your computer so that you can install it on your computer.

After installing µTorrent go to the torrentz website 

http://torrentz.eu

or any other torrent website like Kick ass torrents

http://kickass.to

Then search the books, movies, music or videos you want to download.

After the search click on the torrent link and download it.

Don’t click the direct download.

After the torrent file downloaded, open it with µTorrent or Torch web browser.

Your download will have started automatically.

Constancy

The problem with measuring the motion using displacement, velocity and acceleration is that we can’t predict accurately about the direction and length of the path at every point.

As we have discussed before in displacement, velocity and acceleration, it was considered only the two points of the motion and not all the points in the path. Displacement, velocity and acceleration defined by taking only the initial and the final position vectors of the motion. Position vectors are drawn between only these two points and it depends only on those two.
It has been never cared about “the in between path of the motion” in our definition. It is not sure about whether the motion happens in between path continuously or stops in some of the places. We also don’t know whether the motion slows down or speeds up in some places.
Take an example of travelling in a vehicle. By the way in our travel, we will slow down or speed up or even sometimes will take a break by stopping the vehicle. But from the previous definitions, velocity is defined from the position vectors of just the initial and final position. The motion is taken to be a constant one, as the position vectors and the displacement vectors are taken as straight lines having fixed magnitude of length and direction though it is not true in real.
Since, so much information about the motion has been missed out in our preceding definitions, it is then realized that these definitions are not sufficient for the complete knowledge of mechanics. It needs a mathematical tool. Aimed at the mathematical explanation of motion at every point, it started to try relating all the points in motion. And the relation should be done with our basic definitions.

Try to think it on your own on “how to relate each point in any motion using mathematics and physics??”

The task was completed by two great scientists, Isaac Newton and Gottfried Leibniz. Newton solved the task with physics and physical interpretations. Leibniz solved the same but using the concepts of mathematics.

It is fair to study about the method used by Newton in physics. The principle behind this method is simple but a little has to be understood properly.

The weakness that we are facing in our basic definitions is the matter of instantaneous measurements.
Since we know that our basic definitions are quite right, we just need to improve our methods to get complete information of any motion at every instant.

The problem is there in measurements and not in the definitions.
It can be understood by visualizing the motion as it follows in the topic creation of the term speed,

In our definitions of displacement, velocity, acceleration it is assumed that the displacement vector between two points of the motion is the straight line vector drawn between those two points of motion.

We took the direction as a constant one though the real path of travelling is curved.
 

 
And it cannot be changed the direction of a line, since the direction of a line is a constant one.

But it is started to think in a way whether it is possible to represent a curved path using straight lines.

Task: If it is possible to relate the curved path at each instant to relate with straight lines of positional and displacement vectors, then it will make the task very simple.

Solving the task with mathematics will be studied separately.

In physics it was thought in such a way as follows using constancy,

Constant means nothing but remaining same without any change.

In physics the changings are happening with respect to time. So if any quantity doesn’t change its value with respect to time then it is called ‘constant with respect to time’. In real, all the measurements are done with the help of constancy only. The time of period of this constancy can change but the constancy should happen.
For example take the sentence of saying “the speed of the vehicle is 10 meters per second” though it is not constant for the whole motion. From this sentence we can be damn sure that the vehicle is achieving the constant speed of reaching 10 meters per one second at some instant. But we don’t know whether it stays at the same velocity or not. It is also possible for that object to change its velocity at each instant. Though there are changings with time, in some amount of small time period the vehicle doesn’t change its value.

It can be easily understood from the same vehicle example. Though vehicle is changing its velocities at every instant, in the speedometer the needle crosses all the speeds. It touches a speed at least for a single moment. [Note: It is the same principle that is used in Lagrange’s Mean Value Theorem]

Though the vehicle has continuously changing speeds from 0 to 10 m/s etc. it attains constant values at every small time intervals.
Although the changing of speed is so rapid that it changes with each nano seconds, the constancy happens at every time no matter whether the change is high or low.
It can be noted above that from the 1^st nano second to 2^nd nano second it changes its speed incredibly small amount. But, in the between time period of 1 nano second the vehicle attains some constant velocity. If it is said the change happens in nano seconds, it can be argued the constancy happens in each pico (10^-12) time of intervals. If it is said the change happens in pico seconds, it can be argued the constancy happens in each femto (10^-15) time of intervals.

Hence there is always an argument of constancy in every tiny amount of time intervals.
And it was proclaimed the general mathematical notation for this kind of arguments which is called the Limits.
Instead of arguing by making the time interval so small, we made the general decrement that goes with all type of arguments which is “decreasing the time interval to zero” Or simply “decreasing the intervals to zero”.
And thus the chapter of Limits was formulated and it serves as the fundamental for differentiation and integration.

Here in physics, we used the concept of decreasing time intervals but in Mathematics the same task is finished by considering the problem of the motion in a different mathematical version with the concepts of drawing tangents to the graphs of different functions.
But don’t forget to remember our task as discussed before,

Task: If it is possible to relate the curved path at each instant to relate with straight lines of positional and displacement vectors, then it will make the task very simple.

The mathematical way is discussed completely in the chapter of functions and differentiation in Mathematics.