How to find the speed of joint motion. Types of mechanical movements. Rectilinear movement. Speed ​​and acceleration. Now it's your turn

So, let's say our bodies are moving in the same direction. How many cases do you think there could be for such a condition? That's right, two.

Why does this happen? I am sure that after all the examples you will easily figure out how to derive these formulas.

Got it? Well done! It's time to solve the problem.

Fourth task

Kolya goes to work by car at a speed of km/h. Colleague Kolya Vova is driving at a speed of km/h. Kolya lives kilometers away from Vova.

How long will it take for Vova to catch up with Kolya if they left the house at the same time?

Did you count? Let's compare the answers - it turned out that Vova will catch up with Kolya in an hour or in minutes.

Let's compare our solutions...

The drawing looks like this:

Similar to yours? Well done!

Since the problem asks how long after the guys met, and they left at the same time, the time they drove will be the same, as well as the meeting place (in the figure it is indicated by a dot). When composing the equations, let's take time for.

So, Vova made his way to the meeting place. Kolya made his way to the meeting place. It's clear. Now let's look at the axis of movement.

Let's start with the path that Kolya took. Its path () is shown in the figure as a segment. What does Vova’s path consist of ()? That's right, from the sum of the segments and, where is the initial distance between the guys, and is equal to the path that Kolya took.

Based on these conclusions, we obtain the equation:

Got it? If not, just read this equation again and look at the points marked on the axis. Drawing helps, doesn't it?

hours or minutes minutes.

I hope from this example you understand how important the role is played Well done drawing!

And we smoothly move on, or rather, we have already moved on to the next point of our algorithm - bringing all quantities to the same dimension.

The rule of three "R" - dimension, reasonableness, calculation.

Dimension.

Problems do not always give the same dimension for each participant in the movement (as was the case in our easy problems).

For example, you can find problems where it is said that bodies moved for a certain number of minutes, and their speed of movement is indicated in km/h.

We can’t just take and substitute the values ​​into the formula - the answer will be incorrect. Even in terms of units of measurement, our answer “fails” the reasonableness test. Compare:

Do you see? When multiplying correctly, we also reduce the units of measurement, and, accordingly, we obtain a reasonable and correct result.

What happens if we don’t convert to one measurement system? The answer has a strange dimension and the result is % incorrect.

So, just in case, let me remind you of the meanings of the basic units of length and time.

Length units:

centimeter = millimeters

decimeter = centimeters = millimeters

meter = decimeters = centimeters = millimeters

kilometer = meters

Time units:

minute = seconds

hour = minutes = seconds

day = hours = minutes = seconds

Advice: When converting units of measurement related to time (minutes into hours, hours into seconds, etc.), imagine a clock dial in your head. The naked eye can see that the minutes are a quarter of the dial, i.e. hours, minutes is a third of the dial, i.e. an hour, and a minute is an hour.

And now a very simple task:

Masha rode her bicycle from home to the village at a speed of km/h for minutes. What is the distance between the car house and the village?

Did you count? The correct answer is km.

minutes is an hour, and another minutes from an hour (mentally imagined a clock dial, and said that minutes is a quarter of an hour), respectively - min = hours.

Reasonableness.

You understand that the speed of a car cannot be km/h, unless, of course, we are talking about a sports car? And even more so, it can’t be negative, right? So, rationality, that’s what it’s about)

Calculation.

See if your solution is dimensional and reasonable, and only then check the calculations. It is logical - if there is an inconsistency with dimension and rationality, then it is easier to cross out everything and start looking for logical and mathematical errors.

“Love of tables” or “when drawing is not enough”

Movement problems are not always as simple as we solved before. Very often, in order to solve a problem correctly, you need not just draw a competent picture, but also make a table with all the conditions given to us.

First task

A cyclist and a motorcyclist left at the same time from point to point, the distance between them being kilometers. It is known that a motorcyclist travels more kilometers per hour than a cyclist.

Determine the speed of the cyclist if it is known that he arrived at the point minutes later than the motorcyclist.

This is the task. Pull yourself together and read it several times. Have you read it? Start drawing - a straight line, a point, a point, two arrows...

In general, draw, and now we’ll compare what you got.

It's a bit empty, isn't it? Let's draw a table.

As you remember, all movement tasks consist of the following components: speed, time and path. It is these columns that any table in such problems will consist of.

True, we will add one more column - Name, about whom we write information - a motorcyclist and a cyclist.

Also indicate in the header dimension, in which you will enter the values ​​there. You remember how important this is, right?

Did you get a table like this?

Now let's analyze everything we have and at the same time enter the data into the table and figure.

The first thing we have is the path that the cyclist and motorcyclist took. It is the same and equal to km. Let's bring it in!

Let's take the speed of the cyclist as, then the speed of the motorcyclist will be...

If with such a variable the solution to the problem does not work, it’s okay, we’ll take another one until we reach the winning one. This happens, the main thing is not to be nervous!

The table has changed. We only have one column left unfilled - time. How to find time when there is a path and speed?

That's right, divide the distance by the speed. Enter this into the table.

Now our table is filled in, now we can enter the data into the drawing.

What can we reflect on it?

Well done. Speed ​​of movement of motorcyclist and cyclist.

Let's re-read the problem again, look at the picture and the completed table.

What data is not reflected in the table or figure?

Right. The time the motorcyclist arrived before the cyclist. We know that the time difference is minutes.

What should we do next? That’s right, convert the time given to us from minutes to hours, because the speed is given to us in km/h.

The magic of formulas: drawing up and solving equations - manipulations leading to the only correct answer.

So, as you may have guessed, now we will make up the equation.

Drawing up the equation:

Look at your table, at the last condition that is not included in it and think, the relationship between what and what can we put into the equation?

Right. We can create an equation based on the time difference!

Logical? The cyclist rode more; if we subtract the motorcyclist’s time from his time, we will get the difference given to us.

This equation is rational. If you don’t know what this is, read the topic “”.

We bring the terms to a common denominator:

Let's open the brackets and present similar terms: Phew! Got it? Try your hand at the following problem.

Solution of the equation:

From this equation we get the following:

Let's open the brackets and move everything to the left side of the equation:

Voila! We have a simple quadratic equation. Let's decide!

We received two possible answers. Let's see what we got for? That's right, the speed of the cyclist.

Let us remember the “3P” rule, more specifically “reasonableness”. Do you know what I mean? Exactly! Speed ​​cannot be negative, so our answer is km/h.

Second task

Two cyclists set out on a -kilometer ride at the same time. The first one drove at a speed that was one km/h faster than the second one, and arrived at the finish line hours earlier than the second one. Find the speed of the cyclist who came second to the finish line. Give your answer in km/h.

Let me remind you of the solution algorithm:

• Read the problem a couple of times and understand all the details. Got it?
• Start drawing a picture - in which direction are they moving? how far did they travel? Did you draw it?
• Check that all your quantities are of the same dimension and begin to briefly write out the conditions of the problem, making a table (do you remember what graphs are there?).
• While you are writing all this, think about what to take for? Have you chosen? Write it down in the table! Well, now it’s simple: we make up an equation and solve. Yes, and finally - remember the “3Rs”!
• I've done everything? Well done! I found out that the speed of the cyclist is km/h.

-"What color is your car?" - "She's beautiful!" Correct answers to the questions asked

Let's continue our conversation. So what is the speed of the first cyclist? km/h? I really hope you’re not nodding yes now!

Read the question carefully: “What is the speed of first cyclist?

Do you understand what I mean?

Exactly! Received is not always the answer to the question posed!

Read the questions carefully - perhaps after finding them you will need to perform some more manipulations, for example, add km/h, as in our task.

One more point - often in tasks everything is indicated in hours, and the answer is asked to be expressed in minutes, or all the data is given in km, and the answer is asked to be written in meters.

Watch the dimensions not only during the solution itself, but also when writing down the answers.

Circular movement problems

Bodies in problems can move not necessarily straight, but also in a circle, for example, cyclists can ride along a circular track. Let's look at this problem.

Task No. 1

A cyclist left a point on the circular route. Minutes later, he had not yet returned to the point and the motorcyclist left the point after him. Minutes after setting off, he caught up with the cyclist for the first time, and minutes after that he caught up with him for the second time.

Find the speed of the cyclist if the length of the route is km. Give your answer in km/h.

Solution to problem No. 1

Try to draw a picture for this problem and fill out a table for it. Here's what I got:

Between meetings, the cyclist traveled a distance, and the motorcyclist - .

But at the same time, the motorcyclist drove exactly one lap more, as can be seen from the figure:

I hope you understand that they didn't actually drive in a spiral - the spiral just schematically shows that they drive in a circle, passing the same points on the route several times.

Got it? Try to solve the following problems yourself:

Tasks for independent work:

1. Two motor-cycles start at the same time in one right-hand direction of the two dia-metral-but-pro-ti-on-ways false points of a circular route, the length of which is equal to km. After how many minutes do the cycles become equal for the first time, if the speed of one of them is one km/h higher than the speed of the other? ho-ho?
2. From one point on a circular highway, the length of which is equal to km, at one time there are two motorcyclists in the same direction. The speed of the first motorcycle is equal to km/h, and minutes after the start it was ahead of the second motorcycle by one lap. Find the speed of the second motorcycle. Give your answer in km/h.

Solutions to problems for independent work:

1. Let km/h be the speed of the first motor cycle, then the speed of the second motor cycle is equal to km/h. Let the cycles be equal for the first time in a few hours. In order for the cycles to be equal, the faster one must overcome them from the beginning distance equal to the length of the route.

   We get that the time is hours = minutes.

2. Let the speed of the second motorcycle be equal to km/h. In an hour, the first motorcycle covered more kilometers than the second, so we get the equation:

   The speed of the second motorcyclist is km/h.

Current problems

Now that you are excellent at solving problems “on land,” let’s move into the water and look at the scary problems associated with the current.

Imagine that you have a raft and you lower it into the lake. What's happening to him? Right. It stands because a lake, a pond, a puddle, after all, is still water.

The current speed in the lake is .

The raft will only move if you start rowing yourself. The speed it acquires will be the raft's own speed. It doesn’t matter where you swim - left, right, the raft will move at the speed with which you row. It's clear? It's logical.

Now imagine that you are lowering a raft onto the river, you turn away to take the rope..., you turn around, and it... floats away...

This happens because the river has a current speed, which carries your raft in the direction of the current.

Its speed is zero (you are standing in shock on the shore and not rowing) - it moves at the speed of the current.

Got it?

Then answer this question: “At what speed will the raft float down the river if you sit and row?” Thinking about it?

There are two possible options here.

Option 1 - you go with the flow.

And then you swim at your own speed + the speed of the current. The flow seems to help you move forward.

2nd option - t You are swimming against the current.

Hard? That's right, because the current is trying to “throw” you back. You are making more and more efforts to swim at least meters, respectively, the speed at which you move is equal to your own speed - the speed of the current.

Let's say you need to swim a kilometer. When will you cover this distance faster? When will you go with the flow or against it?

Let's solve the problem and check.

Let's add to our path data on the speed of the current - km/h and the raft's own speed - km/h. How much time will you spend moving with and against the current?

Of course, you coped with this task without difficulty! It takes an hour with the current, and an hour against the current!

This is the whole essence of the tasks at movement with the current.

Let's complicate the task a little.

Task No. 1

The boat with the motor took an hour to travel from point to point, and an hour to return.

Find the speed of the current if the speed of the boat in still water is km/h

Solution to problem No. 1

Let us denote the distance between points as, and the speed of the current as.

We see that the boat takes the same path, respectively:

What did we charge for?

Current speed. Then this will be the answer :)

The speed of the current is km/h.

Task No. 2

The kayak left from point to point located km from. After staying at point for an hour, the kayak went back and returned to point c.

Determine (in km/h) the kayak's own speed if it is known that the speed of the river is km/h.

Solution to problem No. 2

So let's get started. Read the problem several times and make a drawing. I think you can easily solve this on your own.

Are all quantities expressed in the same form? No. Our rest time is indicated in both hours and minutes.

Let's convert this into hours:

hour minutes = h.

Now all quantities are expressed in one form. Let's start filling out the table and finding what we'll take for.

Let be the kayak's own speed. Then, the speed of the kayak downstream is equal and against the current is equal.

Let's write down this data, as well as the path (as you understand, it is the same) and time, expressed in terms of path and speed, in a table:

Let's calculate how much time the kayak spent on its journey:

Did she swim for all the hours? Let's reread the task.

No, not all. She had an hour of rest, so from hours we subtract the rest time, which we have already converted into hours:

h the kayak really floated.

Let's bring all the terms to a common denominator:

Let's open the brackets and present similar terms. Next, we solve the resulting quadratic equation.

I think you can handle this on your own too. What answer did you get? I have km/h.

Let's sum it up

ADVANCED LEVEL

Movement tasks. Examples

Let's consider examples with solutionsfor each type of task.

Moving with the Current

Some of the most simple tasks - river navigation problems. Their whole essence is as follows:

• if we move with the flow, the speed of the current is added to our speed;
• if we move against the current, the speed of the current is subtracted from our speed.

Example #1:

The boat sailed from point A to point B in hours and back again in hours. Find the speed of the current if the speed of the boat in still water is km/h.

Solution #1:

Let us denote the distance between points as AB, and the speed of the current as.

Let's put all the data from the condition into the table:

For each row of this table you need to write the formula:

In fact, you don't have to write equations for each row of the table. We see that the distance traveled by the boat back and forth is the same.

This means that we can equate the distance. To do this, we use immediately formula for distance:

Often you have to use formula for time:

Example #2:

A boat travels a distance of kilometers against the current an hour longer than with the current. Find the speed of the boat in still water if the speed of the current is km/h.

Solution #2:

Let's try to create an equation right away. The time upstream is an hour longer than the time upstream.

It is written like this:

Now, instead of each time, let’s substitute the formula:

We have received an ordinary rational equation, let’s solve it:

Obviously, speed cannot be a negative number, so the answer is km/h.

Relative motion

If some bodies are moving relative to each other, it is often useful to calculate their relative speed. It is equal to:

• the sum of velocities if bodies move towards each other;
• speed differences if bodies move in the same direction.

Example No. 1

Two cars left points A and B simultaneously towards each other at speeds km/h and km/h. In how many minutes will they meet? If the distance between points is km?

I solution method:

Relative speed of cars km/h. This means that if we are sitting in the first car, it seems motionless to us, but the second car is approaching us at a speed of km/h. Since the distance between the cars is initially km, the time it will take for the second car to pass the first:

Method II:

The time from the start of movement to the meeting of the cars is obviously the same. Let's designate it. Then the first car drove the path, and the second - .

In total they covered all the kilometers. Means,

Other movement tasks

Example #1:

A car left point A to point B. At the same time, another car left with him, which drove exactly half the way at a speed of km/h less than the first, and drove the second half of the way at a speed of km/h.

As a result, the cars arrived at point B at the same time.

Find the speed of the first car if it is known that it is greater than km/h.

Solution #1:

To the left of the equal sign we write down the time of the first car, and to the right - of the second:

Let's simplify the expression on the right side:

Let's divide each term by AB:

The result is an ordinary rational equation. Having solved it, we get two roots:

Of these, only one is larger.

Answer: km/h.

Example No. 2

A cyclist left point A of the circular route. Minutes later, he had not yet returned to point A, and a motorcyclist followed him from point A. Minutes after setting off, he caught up with the cyclist for the first time, and minutes after that he caught up with him for the second time. Find the speed of the cyclist if the length of the route is km. Give your answer in km/h.

Solution:

Here we will equate the distance.

Let the speed of the cyclist be, and the speed of the motorcyclist - . Until the moment of the first meeting, the cyclist was on the road for minutes, and the motorcyclist - .

At the same time, they traveled equal distances:

Between meetings, the cyclist traveled a distance, and the motorcyclist - . But at the same time, the motorcyclist drove exactly one lap more, as can be seen from the figure:

I hope you understand that they didn’t actually drive in a spiral; the spiral just schematically shows that they drive in a circle, passing the same points on the route several times.

We solve the resulting equations in the system:

SUMMARY AND BASIC FORMULAS

1. Basic formula

2. Relative motion

• This is the sum of speeds if the bodies move towards each other;
• difference in speed if bodies move in the same direction.

3. Moving with the flow:

• If we move with the current, the speed of the current is added to our speed;
• if we move against the current, the speed of the current is subtracted from the speed.

We helped you deal with movement problems...

Now it's your turn...

If you carefully read the text and solved all the examples yourself, we are willing to bet that you understood everything.

And this is already half the way.

Write below in the comments, have you figured out the movement problems?

Which ones cause the most difficulties?

Do you understand that tasks for “work” are almost the same thing?

Write to us and good luck on your exams!

In previous tasks involving movement in one direction, the movement of bodies began simultaneously from the same point. Let's consider solving problems on movement in one direction, when the movement of bodies begins simultaneously, but from different points.

Let a cyclist and a pedestrian emerge from points A and B, the distance between which is 21 km, and go in the same direction: the pedestrian at a speed of 5 km per hour, the cyclist at 12 km per hour

12 km per hour 5 km per hour

A B

The distance between a cyclist and a pedestrian at the moment they begin to move is 21 km. In an hour of their joint movement in one direction, the distance between them will decrease by 12-5=7 (km). 7 km per hour – speed of approach of a cyclist and a pedestrian:

A B

Knowing the speed of convergence of a cyclist and a pedestrian, it is not difficult to find out how many kilometers the distance between them will decrease after 2 hours, 3 hours of their movement in one direction.

7*2=14 (km) – the distance between a cyclist and a pedestrian will decrease by 14 km in 2 hours;

7*3=21 (km) – the distance between a cyclist and a pedestrian will decrease by 21 km in 3 hours.

With each passing hour, the distance between a cyclist and a pedestrian decreases. After 3 hours, the distance between them becomes equal to 21-21=0, i.e. a cyclist catches up with a pedestrian:

A B

In “catch-up” problems we deal with the following quantities:

1) the distance between points from which simultaneous movement begins;

2) speed of approach

3) the time from the moment the movement begins until the moment when one of the moving bodies catches up with the other.

Knowing the value of two of these three quantities, you can find the value of the third quantity.

The table contains conditions and solutions to problems that can be drawn up for a cyclist to “catch up” with a pedestrian:

Let us express the relationship between these quantities by the formula. Let us denote by the distance between points and, - the speed of approach, the time from the moment of exit to the moment when one body catches up with the other.

In “catch-up” tasks, the speed of approach is most often not given, but it can easily be found from the task data.

Task. A cyclist and a pedestrian left simultaneously in the same direction from two collective farms, the distance between which was 24 km. The cyclist was traveling at a speed of 11 km per hour, and the pedestrian was walking at a speed of 5 km per hour. How many hours after leaving will the cyclist catch up with the pedestrian?

To find how long after leaving the cyclist will catch up with the pedestrian, you need to divide the distance that was between them at the beginning of the movement by the speed of approach; the approaching speed is equal to the difference in speed between the cyclist and the pedestrian.

Solution formula: =24: (11-5);=4.

Answer. After 4 hours the cyclist will catch up with the pedestrian. The conditions and solutions of inverse problems are written in the table:

Each of these problems can be solved in other ways, but they will be irrational in comparison with these solutions.

We have many reasons to thank our God.
Have you noticed how every year, God's organization actively and decisively moves forward with a multitude of gifts!
The heavenly chariot is definitely on the move! At the annual meeting it was said: “If you feel like you can’t keep up with Jehovah’s chariot, buckle up so you don’t get thrown out at the turn!”:)
The prudent servant is seen to ensure continuous movement, opening up new territories for preaching, making disciples, and gaining a fuller understanding of God's purposes.

Since the faithful servant does not rely 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 is evident that when the Governing Body sees a need to clarify any aspect of the truth or to make changes in organizational order, it acts without delay.

Isaiah 60:16 says that God's people will enjoy the milk of the nations, which is advanced technology today.

Today in the hands of the organizationa site that connects and unites us with our brotherhood, and other new products that you probably already know about.

It is only because God sustains and blesses them through his Son and the Messianic Kingdom that these imperfect people can achieve victory over Satan and his wicked system of things.

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 so as to touch the hearts of people of all kinds. After all, how we teach ourselves will determine how we teach others.

In this way we will show that we are deeply concerned about the “desired treasures from 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, being in which we will not lag behind the chariot of Jehovah and will be under the protection of God the Creator, Jehovah (John 6:68).

– Is it worth continuing a relationship if you and your partner have different speeds?

We are sitting in one of the small hotels in Nepal and, according to tradition, we are playing out a question. This is the last day in the mountains and the last time we take anonymous notes. We are 14 people from different countries and cities, we have just completed a trek to the Langtang Valley and Gosaikunda Lake.

Even at the start, in Kathmandu, all the track participants chipped in on an anonymous question. I, the presenter, took one out every evening and read the next problem out loud, which gave rise to discussion, and sometimes even debate, through the prisms of different experiences, understanding of the situation, or misconceptions - an everyday matter.

Our last evening in the mountains has arrived. I once again unfold the piece of paper, read first to myself, and then to everyone:

“Is it worth continuing a relationship if you and your partner have different speeds?”

You can already hear the sound of air being drawn into your lungs. Over the three years of conducting such conversations, the statistics have remained unchanged - questions about relationships have always been the most popular. The group was preparing for a lively discussion.

But everyone was ahead of everyone by that special quiet and calm timbre of voice that only happens to a person who doesn’t have 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 a situation will inevitably come when they change places, of course, if we talk about long-distance relationships.

True, I no longer heard anything - like other opinions, if there were any that evening. Once every couple of years, if I’m lucky, life brings me together with a phrase-book that endlessly unfolds its meaning. One day, something like this was accidentally seen somewhere: “You cannot find yourself, you can only create yourself.” Words that not only stunned me to the core, but also 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 as your partner over a long distance.

I spent a long time spinning around these words, trying to unravel their meaning. I felt the truth behind them. But if with other phrases I only had to push slightly and I was ready to write a whole book, here it didn’t go beyond a pleasant tickle, which is the essence. The texture of my own experience was missing. Then I came to Olga with a request to “return the serve.” Answer my questions that arise around this topic.

Olga responded easily.

About different speeds of movement of partners and relationships over a long distance

Served by Olesya Vlasova, author of the Re-Self blog. Married for 9 months (in a relationship - 3 years). Beats - Olga Vakhrusheva, business consultant, married 32 years. When we met, Olga was 15 and Nikolai was 18 years old. They got married as soon as Olga turned 18. They have been living in New Zealand for 22 years, where they moved from Novosibirsk. Olga and Nikolai have two children and two grandchildren.

– What should the faster one do? From the outside, the story that in a long-distance relationship cannot always have the same speed for both partners sounds beautiful, and most importantly, one feels that there is truth behind these words, but from the inside everything is not so simple and obvious. What should the one who is ahead today do? Should I help the second one? Or vice versa - leave him alone and not “drag him along”? And how to find peace in such a situation?

– For me, the statement that in a long-distance relationship both partners cannot always have the same speed is an axiom. Just like the fact that two people building relationships are a priori different, two independent, unique individuals. Neither is perfect. But this is clear to me now.

When I was younger, I tried to build our family relationships based on previously unviable principles: we must always do everything together and in complete mutual understanding, we must be one, love is a gift that happens to you, which you find if you’re lucky .

In practice, everything turned out to be wrong, of course. And attempts to tie reality to a far-fetched ideal caused misunderstandings, resentment, and quarrels that could have been avoided if the original views of the world had been more viable.

I don’t know what’s going on in young heads now and what ideas your generation grew up on, but in our time, girls from early childhood have seen and heard something like the following:

• In fairy tales and films: a prince on a white horse will definitely gallop to the princess, he will love her more than life itself, they will live happily ever after, and he will solve all her problems.
• From the conversations of older women: a real man should... And further down the list: earn money, 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: there are no real men in the world. You can't count on them. Either they are drunkards, or lazy and henpecked, or heartless careerists. You need to keep everything under control and, in fact, you can trust a man with caution.

So my head is a complete mess of ideas. There is only hope that the ideal relationship will happen on its own or that he will make you happy. But now it’s clear that no one can make another person happy (no matter how hard they try). This is an internal process that runs parallel to steps towards each other.

I return to your main question. What should someone who is faster do today? The answer is I don’t know. There is no universal answer for everyone. Sometimes you need to help, sometimes you need to leave him alone, sometimes you need to give a guiding kick (with love). Often you just need to mind your own business, not panic, but make it clear that you are here, you are nearby and you care 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 reducing speed:

• Difference in temperaments (you have to learn to live with this if you want to save the relationship).
• Health problems that a man often doesn’t talk about, and a woman invents God knows what.
• Problems at work or in business (which he also most often does not talk about until he figures out what to do about it).
• Some big changes that you need to understand before you take the next step.
• The difference in age (and, accordingly, in speed).
• Hormonal changes.
• Finally, fears. Of which men have no less, and maybe even more, than we do, but there is no one to go to for help.

And here we are with our own speeds and personal growth. In general, as my experience shows, this question arises more often among young girls.

- So let's talk about the young girl. She believes (whether this is objective or not is another question), at least it seems to her that she is doing more - taking care of work, children, home. But he doesn't. Does not help. Does less.

- Yes, it's familiar. It seems like he owes me. I earn money, and I also have children. Claims. Expectations. After three years of marriage, it begins - socks in the hallway, he said something wrong, did something wrong.

We need to understand the reasons. Analyze. Is this a temporary decrease in speed or is this the nature of lying on the couch? The second is unlikely to be close to a girl who is active in life. But there may be other reasons. 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 we didn’t voice it at all, but we hope that he will guess it himself). He hasn’t yet had time to comprehend the problem, but we are already rushing to do and solve everything ourselves. Well, why would he then run a race with us? Or why did you tell him about the problem then?

Or he did something, and we are unhappy - he did it wrong. Well, once it’s wrong, the second time it’s wrong, and then you won’t even want to move (would you want to?). Why not pose the question differently: “This is my area of ​​responsibility, and this is yours. How and what you do is your decision, but the expected result is such and such.” He may stumble once, perhaps he will forget, and then he will figure it out. If we believe that he will sort it out, and don’t snort at every point.

This applies to everything. Starting with the basics: instead of declaring with resentment in your voice that he never takes out the trash, and you do everything yourself, by yourself... And you, too, get tired... and further in the text. It’s more productive to say: “Darling, let’s do this: taking out the trash in the house is on you. I'm counting on you." That's all. And forget. And can't stand it. And don't remind me. Even if the house starts to stink. He will also feel it, and remember, and throw it away, and will already remember.

It is also very important to set specific tasks for our partner and ask clearly and clearly for what we need. What are we looking for help with? They simply don't see many things. They don’t even know about their existence at first. And they can’t read our thoughts. It’s much easier to say: “Honey, I’m sewing up in the kitchen, please hang out the laundry and put the kids to bed.” If the man is adequate and is not busy at this moment with something important, then the issue is resolved. What does a young woman usually do? He rushes between the kitchen, laundry and children, waits for him to understand (this is obvious), becomes Satanic, gets offended. Or you could just say it.

The same rules apply in relationships with your son. Apparently, boys perceive such language better.

And it is important to realize such a simple thing that if at the moment a woman (or man) is stronger in a relationship, this does not mean that she (he) is always right.

– What about those who become weaker at some point and can reflect on this? After all, this is also hard. A man, of course, but also a girl capable of introspection will feel uneasy: for some reason she is not in a rut, maybe she’s pregnant, maybe, I don’t know, an illness or something, but he has a career, an upswing, development, movement. This is jealousy, and anxiety, and just a feeling of one’s own worthlessness can come out. Have you ever had this happen?

- Yes, just when moving to New Zealand. From the very beginning we relied on my husband. He had the language, and he immediately went to study and work. I came home tired, but on the rise and with a lot of interesting information, acquaintances, plans. And I felt completely lost. I couldn’t do the simplest things myself (I don’t speak the language, I don’t drive a car, I don’t know how the bank works, I have no friends, my husband can’t provide support - he’s not at home all day, he has two small children in his arms). And a month ago I owned businesses, advised people, taught, taught others what and how to do.

It helped to realize that this was happening to me. That is, it is important not to deceive myself and not to look for those to blame, but to describe with maximum honesty the situation in which I currently find myself.

• What's happening? Where am I now?
• Is this a temporary inconvenience or a real problem?
• How did I end up here?
• What doesn't suit me about the situation?
• What can I do to change the situation?
• Outline real steps.
• Take these steps.
• Check the result with the target and make adjustments if necessary.
• Move on.

In principle, I solve all my problems using this algorithm. The most difficult thing is usually to realize your emotions, remove yourself emotionally from the situation and turn on your head. Sometimes I give myself permission to “be hysterical and feel sorry for myself” for another week, and then get down to business. Usually works.

Trying to ignore your emotions and fears definitely doesn’t work. It’s easier for me to say to myself: “Okay, I’m afraid of this scenario. Fine. Hello, fear." Next, ask yourself the question: “What will happen in the worst case scenario if the fears come true? 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 it’s not really that scary. And then the energy appears to look for options and move on.

The first months in New Zealand were painful: the complete 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 mute “nothing.” But there were children in our arms, so it was impossible to fall into complete hysterics. Therefore, a month later I started learning the language (which is another detective story). Six months later I went to work as a volunteer in a bureau to support poor families (overcame my fear of communication, gained local experience and contacts), and after another six months I started working in my specialty. Well, go ahead.

– What is the most important thing in a long-distance relationship?

— From what I have seen in my life, from communicating with couples who have lived a long life together and are happy together (and, by the way, there are plenty of them, but somehow very little is said about this in modern media, more and more about problems ), – a simple trend emerges very clearly in the relationships of these couples.

All happy couples have mutual trust. I have not seen a single couple where people did not trust each other and lived 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 things are not easy. Mistrust fills their world. From the outside it is clear that the most distrustful person usually has big problems with self-esteem, and besides, he (herself) has sinned precisely in what his half suspects, or had a very bad life experience, or his expectations are very unrealistic.

That is, we return again to the issue of our own fears, unrealistic expectations and other cockroaches in our heads. The partner most often has nothing to do with it at all. You need to understand yourself. In certain cases, you probably need to contact a specialist who can help specific people in a specific situation.

– How can you gain basic trust? Have you worked on this?

“I was lucky: I never lost him.” The feeling of a shoulder and a covered back was fundamental for me from the very beginning of the relationship. And this is what helped me go through different stages, including segments in which we moved at different speeds. I know that my man will never resort to 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 basis 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 issue of lying in relationships arises. The more you strive to control every step of your partner, the more you dream of merging into a single whole and do not leave him personal space, the greater his need to lie and dodge. Sometimes - so as not to disturb you, sometimes - because it’s easier, it happens because you don’t understand how to do it. 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 people who follows 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 your man's decisions. We do not always understand the logic, reasons and expected consequences, but not everything needs to be understood mentally. This is also a necessary component of trust, and I had to learn it.

– Olga, are you and your husband similar? What conclusion do you draw after so many years together?

- No, we are not alike.

- So how to be together 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 on problems and situations. I’m just interested and warm with him. He constantly generates ideas. It makes you look at many things from a different angle and from a different perspective. You begin to understand that there can be different answers to the same question and they both have a right to exist. It is possible to accept that we disagree on some issue. This approach makes life together very interesting and eliminates the grounds for conflict.

This otherness can be enjoyed. Get high. Definitely don’t try to avoid it or smooth it out (tested - doesn’t work). As with everything, the first step is to recognize the ways in which you are different. Does it complement and enrich your shared “we” or are these fundamental differences that make it impossible to be together? If the differences are fundamental and you are incompatible, the answer is clear - the sooner the couple understands this, the better.

If these are just two different “I”s, then what is not the task for personal growth? Learn to enjoy your differences, learn to be flexible, learn to be tolerant of the person closest to you. Probably, you can learn much more when you are around someone who is different. See and recognize yourself from a completely different side.

– You started a relationship at a very early age. And these are colossal personal changes - what you are like at 18, 28 or 48 years old. Completely different people, as a rule. How to continue to love each other despite all these changes?

— While you both are growing, changing, learning, talking about problems, overcoming them together, raising children, doing things together, reading and discussing, relaxing, you are developing a huge joint history, gratitude to each other for the outstretched hand in time, for the warmth, for a hint, for love, for faith... I think that this joint growth only brings us closer together. The main thing is that you talk to each other when something goes wrong, and do not move in fundamentally opposite directions.

“I was preparing for the meeting and with horror I came across the thought of my early youth that divorce is normal. Like, if something goes wrong, it’s 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 absence good examples before my eyes... But I can remember myself at 20 years old, seriously discussing this. And it seems like it’s really normal to separate, if that’s what happened. But something else horrified me - along with thoughts about divorce, there was not a single thought that, in fact, building relationships is much more normal. Working on them, strengthening them, making a conscious contribution, the need to go through difficult areas. Have you instilled thoughts about such work in your children? And how important is it to talk about it?

“I think this is vitally necessary.” It is important to teach this to children, and even better, to show it by example. That is, it’s not enough to talk, you must definitely live your life the way you speak. Children sense falsehood a mile away, and absorb emotions and family atmosphere like sponges. What was torment and search for Nikolai and me becomes obvious things for them.

My children and I talked and talk about this a lot, especially in adolescence and now, when they build their relationships and raise 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 halves.

It would be great if moms and society voiced the following things more often:

• Happy, harmonious relationships do not “happen” - they are built by two loving people.
• Before entering into a long-term relationship, set your expectations. Try to understand what is important to you now and in later life (children - their absence, career - home, life in 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 love my children very much, but this does not mean that I always like them in everything. (Am I clear?)
• He can't always want what you want (and vice versa).
• Your half is not your copy, but another person. Your task is to hear and understand him. Although it will most likely not be possible to fully understand. So accept this difference as a fact of life and don’t try to change it (fundamental 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 definitely returns if the couple does not run away at the first problem situation. And with each such return, the feelings become deeper and more tender (you and I have been 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 don’t count, after the first quarrel it seems that this will never resolve and that this scar is forever. Both you and your partner. Comment from the height of your experience.

– Quarreling without insulting is also a science, this will come with time, but there will also be breakdowns. We perceive the same words differently. One and the same thought can be presented in such a way as to seek a joint solution, or it can be so 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 quarrel happened - because you were tired, sick, overheated, or there is a structural problem in the family that needs to be solved? 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 that meaning into it, that’s not what I meant. There could be anything there - childhood fears, previous negative experiences, incorrect guesses and second 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 you both have calmed down. But leaving such things unthought is dangerous.

On the other hand, it is advisable to learn to take things more simply. (Oh, how long it took for me to understand this.) Don’t try to be perfect, don’t try to build ideal relationships, give yourself and others the right to make mistakes. Understand that it is normal to argue and make peace (the question is how this happens), that there will never be complete mutual understanding (this is a myth). Learn not to make mountains out of molehills. Many “problems” do not need to be corrected or deeply reflected on them; it is better to simply forget (as they say, “we’ve passed, that’s all”).

In short, despite the seriousness of the issue, try not to take 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: “Free your loved ones from your claims and expectations.”

Man: “Don’t forget that your husband is also a person. Don’t blow his mind unless absolutely necessary.”

Somehow like this.

For starters, I want to voice an important idea for me, which is not directly related to your questions and, perhaps, will not cause a resonance yet.

Someday in real life we all face death, come to the edge and realize (not with our minds, but with our hearts) that we are all here temporarily. Both ourselves and the people we love. After such an “insight” (if you don’t hide your head in the sand out of fear), comes a more careful attitude towards yourself and those around you, and the ability to appreciate the banal little things in life, and most importantly, to receive joy and pleasure from them. This makes life beautiful and filled with love. Maybe if you filter your reactions, relationships, problems, fears through the filter of mortality, then many issues that seem serious will go away by themselves.

Hug tightly.

In addition, Olga prepared topics for 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 treks in different parts of Asia. The goal of our programs is to free the mind and body from tension, restore strength and start the rhythm of conscious changes for the better. Our tools are yoga, meditation, freediving, the practice of silence, the right atmosphere for a full transition and the good 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 nearby.

Problems involving motion in one direction refer to one of three main types of motion problems.

Now we will talk about problems in which objects have different speeds.

When moving in one direction, objects can both come closer and move away.

Here we will consider problems involving movement in one direction, in which both objects leave the same point. Next time we will talk about catch-up movement, when objects move in the same direction from different points.

If two objects leave 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, you need to subtract the smaller one from the larger speed:

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If one object leaves one point, and after some time another object leaves in the same direction after it, then they can both approach and move away from each other.

If the speed of an object moving in front is less than the object moving behind it, then the second one catches up with the first one and they get closer.

To find the closing speed, you need to subtract the smaller from the higher speed:

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If the speed of the object that is moving ahead is greater than the speed of the object that is moving behind, then the second one will not be able to catch up with the first one and they will move away from each other.

We find the removal rate in the same way - subtract the smaller one from the higher speed:

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Speed, time and distance are related:

Task 1.

Two cyclists left the same village at the same time in the same direction. The speed of one of them is 15 km/h, the speed of the other is 12 km/h. What distance will be through them after 4 hours?

Solution:

It is most convenient to write the problem conditions 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 leaves from point A to point B. After 2 hours, a car followed 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) speed of approach of a car and a bus

2) 40∙2=80 (km) at this distance from point A there is a 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) the distance 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 at the station. After 2 hours, the cyclist was 12 km ahead of the pedestrian. Find the pedestrian's speed if the cyclist's speed is 10 km/h.

Solution:

1) 12:2=6 (km/h) speed of removal of a cyclist and a pedestrian

2) 10-6=4 (km/h) pedestrian speed.

Answer: 4 km/h.