- Is it worth continuing the relationship if you and your partner have different speeds?
We are sitting in one of the small hotels in Nepal and, by tradition, we are playing a question. This is the last day in the mountains and the last time we pull up anonymous notes. We are 14 people from different countries and cities, we have just completed the trek to the Langtang Valley and to Lake Gosaykunda.
At the start, in Kathmandu, all the members of the track chipped in on an anonymous question. I - the presenter - took out one every evening and read the next problem aloud, which gave rise to a reason for discussion, and sometimes disputes - through the prism of different experiences, understanding the situation, or delusion - a matter of everyday life.
Our last evening in the mountains has come. Once again I unfold the piece of paper, read first to myself, and then to everyone:
"Is it worth continuing the relationship if you and your partner have different speeds?"
The sound of air being drawn into the lungs is already heard. Over the three years of such conversations, the statistics have remained unchanged - questions about relationships have always been the most demanded. The group was preparing for a lively discussion.
But everyone was outstripped by that special quiet and calm timbre of voice, which occurs only in a person who does not need to prove anything:
- My thirty years of experience in marriage suggests that it is impossible to always have the same speed of movement with your partner, - said Olga, one of the participants in our hike. And she continued:
- One way or another, there will be moments when one will be faster and the other slower. And the situation will inevitably come when they switch places, of course, if we talk about long-distance relationships.
True, I have not heard anything - as well as other opinions, if they were at all that evening. Once every couple of years, if I'm lucky, life brings me to a phrase-book that infinitely unfolds its meaning. Once such a phrase became by accident somewhere seen: "One cannot find oneself, one can only create oneself." Words that not only stunned me to the depths of my soul, but literally turned my whole life upside down. That evening was special. I came across another phrase-book that could be read endlessly:
It is impossible to always have the same speed with your partner over a long distance.
I spent a long time then spinning around these words, trying to expand their meaning. I felt the truth behind them. But if with other phrases I had only to push myself off a little, as I was ready to write a whole book, then here it did not go further than a pleasant tickle, which is the point. I lacked the texture of my own experience. Then I came to Olga with a request to "beat off the serve." Answer my questions that arise around the bush about this topic.
Olga responded with ease.
About different speeds of movement of partners and relationships over a long distance
Submitted by Olesya Vlasova, author of the Re-Self blog. Married for 9 months (in a relationship - 3 years). Beats off - Olga Vakhrusheva, business consultant, married for 32 years. When we met, Olga was 15, and Nikolai was 18. They got married as soon as Olga turned 18. For 22 years they have been living in New Zealand, where they moved from Novosibirsk. Olga and Nikolai have two children and two grandchildren.
- What to do to the one who is faster? From the outside, the story that both partners cannot always have the same speed in a long-distance relationship sounds beautiful, and most importantly, one feels that these words are true, but from the inside everything is not so simple and obvious. What about the one who is ahead today? Should I help the second one? Or, on the contrary - to leave him alone and not "drag on himself"? And how to find peace of mind in such a situation?
- For me, the statement that in a long-distance relationship there cannot always be the same speed for both partners is an axiom. As well as the fact that two people building relationships are a priori different, two independent, unique personalities. Both are not perfect. But this is clear to me now.
When I was younger, I tried to build our intrafamily relations based on pre-unviable attitudes: we must always do everything together and in complete understanding, we must be one whole, love is a gift that happens to you, which you find if you're lucky ...
In practice, of course, everything turned out to be wrong. And attempts to tie reality to a far-fetched ideal caused misunderstandings, resentments, and quarrels, which could have been avoided if the original views of the world were more viable.
I do not know what is happening in young heads now and on what ideas your generation grew up, but in our time, girls from early childhood saw and heard something like the following:
- In fairy tales and in films: a prince on a white horse will surely gallop to the princess, he will love her more than life, they will always live happily, and he will solve all her problems.
- From the conversations of older women: a real man should ... And further down the list: earn, provide, be a support, be smart, caring, an excellent father, a loving husband, gentle, understanding, and so on. (in fact, many of these definitions are mutually exclusive).
- From the same source: real men were transferred to the world. You cannot count on them. Either drunkards, or lazy and henpecked, or heartless careerists. You need to keep everything under control and, in fact, you can trust a man with an eye.
So my head is a complete mess of performances. There is only hope that the ideal relationship will happen by itself or he will make you happy. But now it is clear that no one can make another person happy (no matter how hard he tries). This is an internal process that goes in parallel with steps towards each other.
Back to your main question. What should someone who is faster today do? The answer is I don’t know. There is no one-size-fits-all answer. Sometime you need to help, sometime leave alone, sometime set a guiding kick (with love). Often you just need to go about your business, do not panic, but make it clear that you are here, you are there and you worry and love. If we are talking about two adequate people, and not about pathology, then simply understanding that this is not forever usually helps a lot.
In addition, there are often objective reasons for a decrease in speed:
- The difference in temperaments (you have to learn to live with this if you want to keep the relationship).
- Health problems that a man often does not talk about, and a woman invents God knows what.
- Problems at work or in business (which he also usually does not talk about until he figured out what to do about it).
- Some big changes that need to be realized before taking the next step.
- The difference in age (and, accordingly, in speed).
- Hormonal changes.
- Fears, finally. Of which men have no less, and maybe more, than ours, but there is no one to go to for help.
And here we are with our own speed and personal growth. In general, as my experience shows, this question often arises among young girls.
- Let's talk about a young girl. She thinks (objectively or not, it's still a question), at least it seems to her that she is doing more - pulling work, children, home. But he is not. Does not help. Does less.
- Yes, it is familiar. It seems that he owes me. I earn money, and the children are on me. Claims. Expectations. After three years of life together begins - socks in the hallway, either said or did something.
We need to understand the reasons. Analyze. Is it a temporary decrease in speed or is it like lying on the couch? The second is unlikely to be close to an active girl in life. But the reasons may be different. Very often we ourselves do not give our men a chance to get involved in the process.
For example, we voiced the problem (and often did not voice it at all, but we hope that he will guess it himself). He has not yet had time to comprehend the problem, but we are already rushing to do and solve everything ourselves. Well, why should he then run with us in a race? Or - why then did you tell him about the problem?
Or he did something, and we are unhappy - he did something wrong. Well, once it’s not so, the second time it’s not so, and then you don’t want to move (would you want to?). Why not put the question differently: “This is my area of responsibility, and this is yours. How and what you do is your decision, but the result is expected such and such. " He may stumble once, maybe he will forget, and then he will figure it out. If we believe that he will figure it out, and do not snort at every occasion.
This applies to everything. Starting with the elementary: instead of annoyed in his voice to declare that he never takes out the trash, and you do it yourself, yourself ... And you, too, get tired ... and further down the text. It is more productive to say: “Honey, let's do it this way: take out the trash in the house on you. I'm counting on you. " And that's all. And forget. And can't stand it. And not to remind. Even if the house starts to whine. He, too, will feel it, and remember, and throw it out, and will already remember.
It is also very important to set specific tasks for your partner and ask clearly and clearly what we need. In what we are waiting for help. They simply do not see many things. They don't even know about their existence at first. And our thoughts do not know how to read. It's much easier to say, "Honey, I'm stitching up in the kitchen, please hang up the laundry and put the kids to bed." If a man is adequate and is not busy at this moment with something important, then the issue is resolved. And what does a young woman usually do? He rushes between the kitchen, the laundry and the children, waiting for him to understand himself (this is obvious), becoming satanic, offended. And you could just say.
The same rules apply to your relationship with your son. Apparently, boys perceive such language better.
And it is important to realize such a simple thing that if at a given moment in a relationship a woman (or a man) is stronger, this does not mean that she (he) is always right (right).
- And about those who become weaker at some point and can reflect on it? After all, this is also difficult. A man by itself, but also a girl capable of introspection, will feel uneasy: for some reason she is not in a rut, maybe pregnancy, maybe, I don’t know, an illness or something, but he has a career, a rise, development, movement. This is jealousy, and anxiety, and just the feeling of one's own worthlessness can creep out. Have you had this?
- Yes, just when moving to New Zealand. From the very beginning, we relied on my husband. He had a language, and he immediately went to study and work. I came home tired, but on the rise and with a bunch of interesting information, acquaintances, plans. And I felt completely lost. I couldn't do the simplest things myself (I don't have a language, I don't drive a car, how the bank works, I don't know, I have no acquaintances, my husband cannot provide support - he is not at home all day, there are two small children in his arms). And a month ago I owned businesses, consulted people, taught, taught others what to do and how to do it.
The realization that this is happening to me helped. That is, it is important not to deceive yourself and not look for the guilty, but with the utmost honesty describe the situation in which I am at the moment.
- What's happening? Where am I now?
- Is this a temporary inconvenience or a real problem?
- How did I get here?
- What does not suit me in the situation?
- What can I do to change the situation?
- Map out real steps.
- Take these steps.
- Check the result against the target, make corrections, if necessary.
- Move on.
In principle, I solve all my problems using this algorithm. The most difficult thing is usually to become aware of your emotions, take yourself out of the situation emotionally and turn on your head. Sometimes I give myself permission for another week to "try and feel sorry for myself," and then get down to business. Usually works.
Trying to ignore your emotions and fears certainly doesn't work. It's easier for me to say to myself: “Ok, I'm afraid of this scenario. Good. Hello fear. " Then ask yourself the question: “What will happen in the worst case if the fears are justified? Is it deadly? What would be option B? Can I live with this? " Most often, the answer is that you can live with it and not everything is scary in reality. And then the energy appears to look for options and move on.
The first months in New Zealand were painful to be completely zeroed out, the loss of social contacts, status, skills, understanding of how to earn money, how life and society work, the transformation from a sociable professional into a dumb "nothing". But there were children in her arms, so it was impossible to go into complete hysterics. Therefore, after a month I went to learn the language (as - a separate detective story). Six months later, she went to work as a volunteer in a bureau for supporting poor families (she overcame the fear of communication, gained local experience, acquaintances), and six months later she went to work in her specialty. Well, go ahead.
- What is the most important thing in a long-distance relationship?
- From what I have seen in my life, from communication with couples who have lived a long life together and are happy together (and there are plenty of them, by the way, but this is somehow very little said in modern media, more and more about problems ), - a simple tendency is very clear in the relationship of these couples.
All happy couples have mutual trust. I have not seen a single couple so that people do not trust each other and live happily. It is impossible to live with a person and constantly expect a catch. This is a life of endless fear and stress. For both.
I also know couples where everything is not easy. Mistrust fills their world. From the outside, it can be seen that the most distrustful one usually has big problems with self-esteem, and besides, he himself (herself) is guilty of exactly what he suspects his half of, or had a very bad life experience, or the expectations are very unrealistic.
That is, we again return to the question of our own fears, unrealistic expectations and other cockroaches in our heads. The partner most often has nothing to do with it. You need to deal with yourself. In certain cases, you probably need to contact a specialist who can help specific people in a specific situation.
- How can one gain basic trust? Have you worked on this?
- I was lucky: I never lost it. The feeling of a shoulder and a covered back was fundamental for me from the very beginning of the relationship. And it was this that helped me to go through different stages, including the sections on which we moved at different speeds. I know that my man will never go for deep, thoughtful meanness, that he will act in accordance with his basic principles and his nature. So I perceive any problems and misunderstandings as problems and misunderstandings. If the base is trust and the absence of a knife in the back, then everything else can be solved. I guess I can say that my trust is a choice. And I do it every day.
- And jealousy?
- If, deep down, you understand that anything can happen in life, and you are ready to let your man go in a situation where his happiness will be somewhere else, then the reason for jealousy disappears.
In this regard, the question of lies in relationships arises. The more you strive to control each step of your partner, the more you dream of merging into a single whole and do not leave him personal space, the more he needs to lie and dodge. Sometimes - so as not to disturb you, sometimes - because it is easier, it happens because you do not understand how it should be. I know from myself as a child. I grew up with an extremely controlling mother, where the forces were unequal, and I am not one of those who follow the lead. So, if possible, save your loved one from the very need to lie, give him space, the opportunity not to answer all the questions you ask and not to report on every step. The more you believe in your man and in your man, the better and more comfortable you both are.
It is very important to learn to respect the decisions of your man. We do not always understand the logic, causes and expected consequences, but not everything needs to be understood intellectually. This is also a necessary component of trust, and this had to be learned.
- Olga, do you and your husband look alike? What is your conclusion after so many years together?
- No, we are not alike.
- So how to be with someone who is not like you? What to do with this dissimilarity?
- We are not alike, but we complement each other. I am very interested in his view of problems and situations. I'm just interested and warm with him. He is constantly generating ideas. He makes many things look from a different angle and from the other side. You begin to understand that there can be different answers to the same question, and they both have a right to exist. We can accept that we disagree on some issue. This approach makes life together very interesting and deprives the cause of conflict.
This dissimilarity can be enjoyed. Get high. Definitely not trying to avoid or smooth it out (tested - doesn't work). As with everything, the first step is to recognize where you are not alike. Does this complement and enrich your shared "we" or are these fundamental differences that are impossible to be together with? If the differences are fundamental and you are incompatible, the answer is clear - the sooner a couple understands this, the better.
If these are just two different "I", then why not a task for personal growth? Learn to enjoy your differences, learn to be flexible, learn to be tolerant of the closest person. Probably, next to the dissimilar, you can learn much more. See and get to know yourself from a completely different perspective.
- You started a relationship at a very early age. And these are colossal personal changes - the way you are at 18, at 28 or at 48 years old. Completely different people, as a rule. How can we continue to love each other despite all these changes?
- While both of you are growing, changing, learning, talking about problems, overcoming them together, raising children, doing a joint work, reading and discussing, relaxing, you are developing a huge joint story, gratitude to each other for the hand outstretched in time, for the warmth, for a hint, for love, for faith ... I think that this joint growth only brings us closer. The main thing is that you talk to each other when something went wrong, and do not move in fundamentally opposite directions.
- I was preparing for the meeting and with horror stumbled upon the thought of my early youth that divorce is normal. Like, if something goes wrong - a divorce. This is fine. I don't know what it was. Or the consequences of an era when a new level of openness and accessibility created this trend. Or the lack of good examples before my eyes ... But I can remember myself as a 20-year-old, seriously talking about this. And it seems like it's really okay to disperse, if it really happened. But something else terrified me - along with thinking about divorces, there was not a single thought that, in fact, building relationships is much more normal. Working on them, strengthening, making a conscious contribution, the need to go through difficult sections. Have you instilled thoughts about such work in your children? And how important is it to talk about it?
- I think it is vital. It is important to teach children this, and even better - to show by example. That is, it is not enough to say, it is imperative to live your life as you say. Children feel false a mile away, and absorb emotions and family atmosphere like sponges. What was a torment and a search for Nikolai and me becomes obvious things for them.
My children and I talked and talk a lot about this, especially in adolescence and now, when they are building their relationships and raising their children. By the way, both say that at some point our example caused difficulties, since the bar was set too high. What is obvious and understandable to them is not obvious to their other half.
It would be great if moms and society more often voiced such things:
- Happy, harmonious relationships don't "happen" - they are built by two loving people.
- Before entering into a long-term relationship, define your expectations. Try to understand what is important for you now and in future life (children - their absence, career - home, life in a big city - on an island in the ocean, gentle - grasping). It is clear that this will all change many times, but trying to understand your life priorities helps a lot.
- Check the coordinates with your chosen one. Do you agree on the most important issues?
- Your half is a living person, not an ideal. With all the ensuing consequences. In certain situations, you may not like him, and this is normal and does not mean the death of the relationship. It's like with children. I really love my children, but this does not mean that I always like them and in everything. (Do I understand it?)
- He may not always want what you want (and vice versa).
- Your half is not your copy, but the other person. Your task is to hear and understand it. Although it will most likely not be fully understood. So take this difference as a fact of life and don't try to redo it (basic personality traits, I'm not talking about socks in the hallway).
- The state of happiness and harmony in a relationship is not constant. It comes and goes, but it certainly comes back if the couple does not scatter at the first problem situation. And with each such return, feelings become deeper and more tender (we have gone through so much together, we have already understood so much about each other).
- Before the first quarrel, it seems that the relationship will always be smooth, small roughnesses do not count, after the first quarrel it seems that it will never go away and that this scar is forever. Both you and your partner. Comment from the height of your experience.
- To quarrel without offending is also a science, it will come with time, but there will also be breakdowns. We perceive the same words in different ways. One and the same thought can be presented in such a way as to seek a joint solution, or it can be done in such a way that both will lick the scars. The tone is important, the moment is important, how the phrase is constructed is important. You need to understand why the fight happened - because you are tired, sick, overheated, or is there a structural problem in the family that needs to be addressed? It is very important not to get personal. We women suffer from this often.
What can we do about it? How to avoid such passions in the future? How can we talk about a sick person without offending or blaming? Why did you (me) have such a reaction to the remark (question)? I didn’t put such a meaning into it, I didn’t mean it. There can be anything - childhood fears, previous negative experiences, wrong guesses and thinking out thoughts, our tone and construction of the question. We need to talk about this. Often not immediately, but when the fuse has cooled down and both of you have calmed down. But leaving such things unimaginable is dangerous.
On the other hand, it is desirable to learn how to treat everything easier. (Oh, how long did it get to me.) Not trying to be perfect, not trying to build perfect relationships, giving yourself and others the right to make mistakes. To understand that swearing and putting up is normal (the question is how it happens), that there will never be a complete understanding (this is a myth). Learn not to make an elephant out of a fly. Many "problems" do not need to be corrected or deeply reflected about them, it is better to simply forget (as they say, "we passed, and that's it").
In short, for all the seriousness of the issue, try not to take your life together and relationships too seriously. And there is no need to persistently and endlessly improve everything (yourself, him, relationships), often our imperfections are the highlight that keeps us together.
Woman: "Deliver your loved ones from their claims and expectations."
Man: “Don't forget that your husband is also human. Do not take his brains out unless absolutely necessary. "
Somehow like this.
For a snack, I want to voice an important thought for me, which does not directly relate to your questions and, perhaps, until it causes a resonance.
Sometime in real life, we all face death, come to the edge and realize (not with our mind, but with our heart) that we are all here temporarily. Both themselves and the people we love. After such "insight" (if you do not hide your head in the sand from fear) comes a more careful attitude towards yourself and those who are nearby, and the ability to appreciate the banal little things in life, and most importantly - to get joy and pleasure from them. It makes life beautiful and filled with love. Maybe if you filter your reactions, relationships, problems, fears through the filter of mortality, then many questions that seem serious will go away by themselves.
Hug tightly.
In addition to the topic, Olga prepared for an independent analysis in the field of relationships and a better understanding of both herself and her man.
Olesya Vlasova
P.S. Friends, for 5 years now we have been conducting retreats, expeditions and mountain tracks in different parts of Asia. The goal of our programs is to release the mind and body from tension, restore strength and launch the rhythm of conscious changes for the better. Our tools are yoga, meditation, freediving, the practice of silence, the right atmosphere for full-fledged switching, and a kind company of like-minded people. If you were looking for a place where you can fully switch and qualitatively rethink the current "settings" - we are here.
We have many reasons to thank our God.
Have you noticed how in every year, actively and decisively, God's organization is accelerating its pace by providing many gifts!
The celestial chariot is definitely on the move! At the annual meeting, it was reported: "If you think that you are not able to keep up with Jehovah's chariot, buckle up so that you do not fly out at the bend!" :)
It can be seen how the discreet slave ensures continuous movement, opening new territories for preaching, preparing disciples, and gaining a more complete understanding of God's purposes.
Since the faithful slave relies not on human strength, but on the guidance of the holy spirit, it is clear that the faithful servant is led by God's spirit !!!
It can be seen that when the Governing Body sees a need to clarify an aspect of the truth or to make organizational changes, it acts without delay.
Isaiah 60:16 says that God's people will enjoy the milk of the nations, which is the leading technology today.
Today in the hands of the organizationa site that connects and unites us with our brotherhood, and other novelties that you probably already know about.
It is only because God supports and blesses them through his Son and the Messianic Kingdom that these imperfect humans can triumph over Satan and his wicked system of things.
Compare the 2014, 2015, 2016 circulation and language counts of the December and January issues of The Watchtower and Awake magazines.
And below 1962.
The Watchtower magazine is in blue, and the Awake magazine is in red.
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The Watchtower's circulation has grown to 58.987 million since January 2015 and is already being translated into 254 languages. On the front page of this magazine, there was also an outline for the ministry presentation.
Incredible! And they say that miracles do not happen! Such a circulation is a real miracle!
What our publications have!
Since last August (2014), our site's rating has grown by 552 positions, thus improving by 30 percent.
For non-commercial sites, this is an unconditional record.A little more and we will be able to enter the top 1000 !!!
Why are they doing this?
Imagine a sinking ship. There are, among other things, three groups of people.
The first try to feed the passengers.
The second offer warm fur coats.
Still others help to get into the boats and get out of the ship.
Everyone seems to be doing good. But what kind of goodness makes sense in this situation? The answer is obvious! What's the point if someone is fed, clothed, and he will die anyway. First you need to transfer from the sinking ship and get to a safe place, and then feed and heat.
Jehovah's Witnesses do the same - they do good to people that makes sense.
While this material-centered world is wasting away from spiritual hunger, let us develop an appetite for spiritual food.
Let's not fall into the trap of materialism!
Paul pointed out THREE TIMES to whom and how we should show concern?
1Tm 2: 1 Prayers should be offered up “for people of all kinds”
1tm 2: 4 It is necessary "that people of all kinds ... come to an accurate knowledge of the truth."
1tm 2: 6 Christ "gave himself as a ransom for all"
What will help us to show deep concern for all and reach people of all kinds by preaching?
This requires one very important quality that Jehovah possesses - impartiality! ( Ac 10:34)
Truly, Jehovah is "impartial" (attitude) and "shows no respect for anyone" (actions)
Jesus preached to people of all kinds. Remember, in his examples, Jesus spoke of people of different backgrounds and social backgrounds: a farmer sowing a seed, a housewife making bread, a man working in a field, a prosperous merchant who sells pearls, hard-working fishermen who cast their nets. (Mt 13: 31-33, 44-48)
Fact: Jehovah and Jesus want “people of all kinds to be saved” and receive eternal blessings. They don't put some people above others.
A lesson for us: To imitate Jehovah and Jesus, we need to preach to people of all kinds, regardless of race or life circumstances.
The Organization of God has already done a lot for those who speak a foreign language, immigrants, students, refugees, those who live in nursing homes, in gated complexes, entrepreneurs, prisoners, deaf, blind, adherents of non-Christian religions and others.
] At present, 578 congregations are assigned to preach the good news in correctional institutions, which are assigned to them, under the supervision of a branch of 578 congregations in Russia. Many of these locations have hosted congregation meetings, group and personal Bible studies. Preaching in such places helps many to “put on a new personality” and serve the true God, Jehovah. Yes, it is important to continue sanctifying the name of God!
Therefore, let us appreciate everything that happens in God's organization. Let us learn to skillfully use the publications issued by the faithful slave, which are designed in such a way as to touch the hearts of people of all kinds. After all, how we teach ourselves, it will depend on how we teach others.
In this way, we will show that we show deep concern for the “coveted treasures of all nations” that still need to be brought.
Surely we, like Peter, have learned the lesson:
“we have nowhere to go” - there is only one place in which we will keep up with Jehovah's chariot and will be under the protection of God the Creator, Jehovah (John 6:68).
2. BODY SPEED. STRAIGHT AND UNIFORM MOTION.
Speed Is a quantitative characteristic of body movement.
average speed Is a physical quantity equal to the ratio of the point displacement vector to the time interval Δt during which this displacement occurred. The direction of the average velocity vector coincides with the direction of the displacement vector. Average speed is determined by the formula:
Instant speed, that is, the speed at a given moment in time is a physical quantity equal to the limit to which the average speed tends with an infinite decrease in the time interval Δt:
In other words, the instantaneous speed at a given moment in time is the ratio of a very small movement to a very small time interval during which this movement occurred.
The instantaneous velocity vector is directed tangentially to the trajectory of the body's motion (Fig. 1.6).
Rice. 1.6. Instantaneous velocity vector.
In the SI system, speed is measured in meters per second, that is, the unit of speed is considered to be the speed of such a uniform rectilinear motion, in which in one second the body travels a path of one meter. The speed unit is denoted m / s... Velocity is often measured in other units. For example, when measuring the speed of a car, train, etc. the commonly used unit is kilometer per hour:
1 km / h = 1000 m / 3600 s = 1 m / 3.6 s
1 m / s = 3600 km / 1000 h = 3.6 km / h
Speed addition (perhaps not necessarily the same question will be in 5).
The velocities of body movement in different reference frames are linked by the classical speed addition law.
Body speed relative stationary frame of reference is equal to the sum of the body's velocities in moving frame of reference and the most mobile frame of reference relative to the stationary one.
For example, a passenger train travels on a railroad at a speed of 60 km / h. A person walks along the carriage of this train at a speed of 5 km / h. If we consider the railway stationary and take it as a reference system, then the speed of a person relative to the reference system (that is, relative to the railway) will be equal to the addition of the speeds of the train and the person, that is
60 + 5 = 65 if the person goes in the same direction as the train
60 - 5 = 55 if the person and the train are moving in different directions
However, this is only true if the person and the train are moving along the same line. If a person moves at an angle, then this angle will have to be taken into account, remembering that speed is vector quantity.
The example is highlighted in red + The law of addition of displacement (I think this does not need to be learned, but for general development you can read it)
Now let's look at the example described above in more detail - with details and pictures.
So, in our case, the railway is fixed frame of reference... The train that moves this road is moving frame of reference... The carriage on which the person is walking is part of the train.
The speed of a person relative to the car (relative to the moving frame of reference) is 5 km / h. Let us denote it by the letter Ch.
The speed of the train (and hence the carriage) relative to the stationary frame of reference (that is, relative to the railroad) is 60 km / h. Let us denote it by the letter B. In other words, the speed of the train is the speed of the moving frame of reference relative to the stationary frame of reference.
The speed of a person relative to the railway (relative to a stationary frame of reference) is still unknown to us. Let's designate it with a letter.
Let's connect the XOY coordinate system with the stationary reference system (Fig. 1.7), and the X P O P Y P. coordinate system with the moving reference system. Now let's try to find the speed of a person relative to the stationary reference system, that is, relative to the railroad.
In a short time interval Δt, the following events occur:
Then, during this period of time, the movement of a person relative to the railway:
This is addition law of displacements... In our example, the movement of a person relative to the railroad is equal to the sum of the movements of a person relative to the carriage and the carriage relative to the railroad.
Rice. 1.7. The law of addition of displacements.
The law of addition of displacements can be written as follows:
= Δ H Δt + Δ B Δt
The speed of a person relative to the railroad is:
Person's speed relative to the car:
Δ H = H / Δt
Car speed relative to the railroad:
Therefore, the speed of a person relative to the railway will be equal to:
This is the lawspeed addition:
Uniform movement- this is movement with constant speed, that is, when the speed does not change (v = const) and acceleration or deceleration does not occur (a = 0).
Straight motion Is movement in a straight line, that is, the trajectory of a rectilinear movement is a straight line.
Uniform rectilinear movement- This is a movement in which the body makes the same movements for any equal intervals of time. For example, if we divide some time interval into segments of one second, then with uniform motion, the body will move the same distance for each of these segments of time.
The speed of uniform rectilinear movement does not depend on time and at each point of the trajectory is directed in the same way as the movement of the body. That is, the displacement vector coincides in direction with the velocity vector. In this case, the average speed for any period of time is equal to the instantaneous speed:
Uniform straight motion speed Is a physical vector quantity equal to the ratio of the body's displacement over any time interval to the value of this interval t:
Thus, the speed of uniform rectilinear motion shows how much a material point moves per unit of time.
Moving with uniform rectilinear motion is determined by the formula:
Distance traveled in rectilinear motion it is equal to the displacement modulus. If the positive direction of the OX axis coincides with the direction of motion, then the projection of the velocity onto the OX axis is equal to the magnitude of the velocity and is positive:
v x = v, that is, v> 0
The projection of displacement on the OX axis is equal to:
s = vt = x - x 0
where x 0 is the initial coordinate of the body, x is the final coordinate of the body (or the coordinate of the body at any time)
Equation of motion, that is, the dependence of the coordinates of the body on time x = x (t) takes the form:
If the positive direction of the OX axis is opposite to the direction of motion of the body, then the projection of the body's velocity onto the OX axis is negative, the velocity is less than zero (v< 0), и тогда уравнение движения принимает вид.
§ 1 Formula of simultaneous movement
We come across the formulas of simultaneous movement when solving problems of simultaneous movement. The ability to solve a particular movement problem depends on several factors. First of all, it is necessary to distinguish between the main types of tasks.
Tasks for simultaneous movement are conventionally divided into 4 types: tasks for oncoming movement, tasks for movement in opposite directions, tasks for movement in pursuit and tasks for movement with a lag.
The main components of these types of tasks are:
distance traveled - S, speed - ʋ, time - t.
The relationship between them is expressed by the formulas:
S = ʋ t, ʋ = S: t, t = S: ʋ.
In addition to the named main components, when solving problems on movement, we can encounter such components as: the speed of the first object - ʋ1, the speed of the second object - ʋ2, the speed of approach - ʋsbl., The speed of removal - sp., The meeting time - tintr., The initial distance - S0, etc.
§ 2 Tasks for oncoming traffic
When solving problems of this type, the following components are used: the speed of the first object - ʋ1; the speed of the second object is ʋ2; approach speed - ʋsbl .; time before meeting - tvstr .; path (distance) traveled by the first object - S1; the path (distance) traveled by the second object - S2; the entire path traveled by both objects - S.
The relationship between the components of oncoming traffic tasks is expressed by the following formulas:
1. The initial distance between objects can be calculated using the following formulas: S = ʋsbl. · Tvr. or S = S1 + S2;
2.the approach speed is found by the formulas: ʋsbl. = S: tintr. or ʋsbl. = ʋ1 + ʋ2;
3.The meeting time is calculated as follows:
Two ships sail towards each other. The speed of the motor ships is 35 km / h and 28 km / h. How long will it take for them to meet if the distance between them is 315 km?
ʋ1 = 35 km / h, ʋ2 = 28 km / h, S = 315 km, tintr. =? h.
To find the time of the meeting, you need to know the initial distance and the speed of approach, since tvr. = S: ʋsbl. Since the distance is known by the problem statement, we find the approach speed. ʋsbl. = ʋ1 + ʋ2 = 35 + 28 = 63 km / h. Now we can find the required meeting time. tint = S: ʋsbl = 315: 63 = 5 hours. We got that the ships will meet in 5 hours.
§ 3 Tasks for the movement in pursuit
When solving problems of this type, the following components are used: the speed of the first object - ʋ1; the speed of the second object is ʋ2; approach speed - ʋsbl .; time before meeting - tvstr .; path (distance) traveled by the first object - S1; the path (distance) traveled by the second object - S2; the initial distance between objects is S.
The scheme for tasks of this type is as follows:
The relationship between the components of the pursuit tasks is expressed by the following formulas:
1.The initial distance between objects can be calculated using the following formulas:
S = ʋsbl. Tintr. Or S = S1 - S2;
2.the approach speed is found by the formulas: ʋsbl. = S: tintr. or ʋsbl. = ʋ1 - ʋ2;
3.The meeting time is calculated as follows:
tint = S: sl., Tintr. = S1: ʋ1 or tintr. = S2: ʋ2.
Let's consider the application of these formulas on the example of the following problem.
The tiger chased after the deer and caught up with him after 7 minutes. What is the initial distance between them if the speed of the tiger is 700 m / min and the speed of the deer is 620 m / min?
ʋ1 = 700 m / min, ʋ2 = 620 m / min, S =? m, tvstr. = 7 minutes
To find the initial distance between a tiger and a deer, it is necessary to know the time of meeting and the speed of convergence, since S = tstr. · Sbl. Since the meeting time is known from the problem statement, we find the approach speed. ʋsbl. = ʋ1 - ʋ2 = 700 - 620 = 80 m / min. Now we can find the desired initial distance. S = tintr. · Sbl = 7 · 80 = 560 m. We found that the initial distance between the tiger and the deer was 560 meters.
§ 4 Problems for movement in opposite directions
When solving problems of this type, the following components are used: the speed of the first object - ʋ1; the speed of the second object is ʋ2; removal rate - ud; travel time - t .; path (distance) traveled by the first object - S1; the path (distance) traveled by the second object - S2; initial distance between objects - S0; the distance that will be between objects after a certain time is S.
The scheme for tasks of this type is as follows:
The relationship between the components of tasks for movement in opposite directions is expressed by the following formulas:
1.The final distance between objects can be calculated using the following formulas:
S = S0 + ʋsp. T or S = S1 + S2 + S0; and the initial distance - according to the formula: S0 = S - sp. · T.
2.The rate of removal is found by the formulas:
ʋud. = (S1 + S2): t orʋud. = ʋ1 + ʋ2;
3. Travel time is calculated as follows:
t = (S1 + S2): sp., t = S1: ʋ1 or t = S2: ʋ2.
Let's consider the application of these formulas on the example of the following problem.
Two cars left the car parks simultaneously in opposite directions. The speed of one is 70 km / h, the other is 50 km / h. What is the distance between them in 4 hours if the distance between the fleets is 45 km?
ʋ1 = 70 km / h, ʋ2 = 50 km / h, S0 = 45 km, S =? km, t = 4 h.
To find the distance between cars at the end of the path, you need to know the travel time, the initial distance and the speed of removal, since S = sp. · T + S0 Since the time and the initial distance are known from the problem statement, we find the removal rate. ʋud. = ʋ1 + ʋ2 = 70 + 50 = 120 km / h. Now we can find the required distance. S = ud. T + S0 = 120 4 + 45 = 525 km. We got that in 4 hours there will be a distance of 525 km between cars
§ 5 Tasks for movement with a lag
When solving problems of this type, the following components are used: the speed of the first object - ʋ1; the speed of the second object is ʋ2; removal rate - ud; travel time - t .; initial distance between objects - S0; the distance that will become between objects after a certain amount of time - S.
The scheme for tasks of this type is as follows:
The relationship between the components of lagging tasks is expressed by the following formulas:
1. The initial distance between objects can be calculated by the following formula: S0 = S - sp. · T; and the distance that will become between objects after a certain time - according to the formula: S = S0 + sp. · T;
2.The speed of removal is found by the formulas: sp. = (S - S0): t or sp. = ʋ1 - ʋ2;
3. Time is calculated as follows: t = (S - S0): sp.
Let's consider the application of these formulas using the example of the following problem:
Two cars drove out of two cities in the same direction. The speed of the first is 80 km / h, the speed of the second is 60 km / h. In how many hours will there be 700 km between cars if the distance between cities is 560 km?
ʋ1 = 80 km / h, ʋ2 = 60 km / h, S = 700 km, S0 = 560 km, t =? h.
To find the time, you need to know the initial distance between objects, the distance at the end of the path and the speed of removal, since t = (S - S0): sp. Since both distances are known by the condition of the problem, we find the speed of removal. ʋud. = ʋ1 - ʋ2 = 80 - 60 = 20 km / h. Now we can find the required time. t = (S - S0): ʋsp = (700 - 560): 20 = 7h. We got that in 7 hours there will be 700 km between cars.
§ 6 Brief summary on the topic of the lesson
With the simultaneous oncoming movement and movement in pursuit, the distance between two moving objects decreases (before the meeting). For a unit of time, it decreases by ʋsbl., And for the entire time of movement before the meeting, it will decrease by the initial distance S. Hence, in both cases, the initial distance is equal to the speed of approach multiplied by the time of movement before the meeting: S = ʋsbl. · Tvstr .. The only difference is that with oncoming traffic ʋsbl. = ʋ1 + ʋ2, and when moving after ʋsbl. = ʋ1 - ʋ2.
When moving in opposite directions and with a lag, the distance between the objects increases, so the meeting will not occur. For a unit of time it increases by ud., And for the entire time of movement it will increase by the value of the product ʋud. · T. This means that in both cases the distance between the objects at the end of the path is equal to the sum of the initial distance and the product ʋsp · t. S = S0 + sp. T. The only difference is that with the opposite motion sp. = ʋ1 + ʋ2, and when moving with a lag ʋsp. = ʋ1 - ʋ2.
List of used literature:
- Peterson L.G. Mathematics. 4th grade. Part 2. / L.G. Peterson. - M .: Juventa, 2014 .-- 96 p.: Ill.
- Mathematics. 4th grade. Methodical recommendations for the textbook of mathematics "Learning to learn" for grade 4 / L.G. Peterson. - M .: Juventa, 2014 .-- 280 p.: Ill.
- Zak S.M. All tasks for the mathematics textbook for grade 4 L.G. Peterson and a set of independent and control works. FSES. - M .: YUNVES, 2014.
- CD-ROM. Mathematics. 4th grade. Scripts of lessons for the textbook for part 2 Peterson L.G. - M .: Juventa, 2013.
Images used:
One-way motion problems are one of three main types of motion problems.
Now we will talk about tasks in which objects have different speeds.
When moving in one direction, objects can both approach and move away.
Here we will consider tasks for movement in one direction, in which both objects leave the same point. Next time we will talk about chasing, when objects move in the same direction from different points.
If two objects left the same point at the same time, then, since they have different speeds, the objects move away from each other.
To find the removal rate, subtract the lower rate from the higher rate:
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If one object left one point, and after a while another object followed it in the same direction, then they can both approach and move away from each other.
If the speed of the object moving in front is less than the object moving after it, then the second catches up with the first and they approach each other.
To find the approach speed, subtract the lower one from the higher speed:
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If the speed of the object that is in front is greater than the speed of the object that follows, then the second will not be able to catch up with the first and they move away from each other.
We find the removal speed in the same way - subtract the lower one from the higher speed:
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Speed, time and distance are related:
Objective 1.
Two cyclists left one village in one direction at the same time. The speed of one of them is 15 km / h, the speed of the other is 12 km / h. What is the distance through them in 4 hours?
Solution:
The problem condition is most conveniently written in the form of a table:
1) 15-12 = 3 (km / h) speed of removal of cyclists
2) 3 ∙ 4 = 12 (km) this distance will be between cyclists in 4 hours.
Answer: 12 km.
A bus departed from point A to point B. After 2 hours, a car drove out after him. At what distance from point A will the car catch up with the bus, if the speed of the car is 80 km / h, and the speed of the bus is 40 km / h?
1) 80-40 = 40 (km / h) the speed of convergence of a car and a bus
2) 40 ∙ 2 = 80 (km) at this distance from point A is the bus when the car leaves A
3) 80: 40 = 2 (h) time after which the car will catch up with the bus
4) 80 ∙ 2 = 160 (km) distance that the car will travel from point A
Answer: at a distance of 160 km.
Problem 3
A pedestrian and a cyclist left the village at the same time. After 2 hours, the cyclist was 12 km ahead of the pedestrian. Find the speed of the pedestrian if the speed of the cyclist is 10 km / h.
Solution:
1) 12: 2 = 6 (km / h) speed of removal of the cyclist and pedestrian
2) 10-6 = 4 (km / h) pedestrian speed.
Answer: 4 km / h.
