Mechanical movement is represented graphically. The dependence of physical quantities is expressed using functions. Designate

Uniform motion graphs

Dependence of acceleration on time. Since during uniform motion the acceleration is zero, the dependence a(t) is a straight line that lies on the time axis.

Dependence of speed on time. The speed does not change over time, the graph v(t) is a straight line parallel to the time axis.

The numerical value of the displacement (path) is the area of ​​the rectangle under the speed graph.

Dependence of the path on time. Graph s(t) - sloping line.

The rule for determining speed from the graph s(t): The tangent of the angle of inclination of the graph to the time axis is equal to the speed of movement.

Graphs of uniformly accelerated motion

Dependence of acceleration on time. Acceleration does not change with time, has a constant value, the graph a(t) is a straight line parallel to the time axis.

Dependence of speed on time. With uniform motion, the path changes according to a linear relationship. In coordinates. The graph is a sloping line.

The rule for determining the path using the graph v(t): The path of a body is the area of ​​the triangle (or trapezoid) under the velocity graph.

The rule for determining acceleration using the graph v(t): The acceleration of a body is the tangent of the angle of inclination of the graph to the time axis. If the body slows down, the acceleration is negative, the angle of the graph is obtuse, so we find the tangent of the adjacent angle.

Dependence of the path on time. During uniformly accelerated motion, the path changes according to

« Physics - 10th grade"

How does uniform motion differ from uniformly accelerated motion?
How does the path graph for uniformly accelerated motion differ from the path graph for uniform motion?
What is the projection of a vector onto any axis?

In the case of uniform rectilinear motion, you can determine the speed from a graph of the coordinates versus time.

The velocity projection is numerically equal to the tangent of the angle of inclination of the straight line x(t) to the abscissa axis. Moreover, the higher the speed, the greater the angle of inclination.

Rectilinear uniformly accelerated motion.

Figure 1.33 shows graphs of the projection of acceleration versus time for three different values ​​of acceleration for rectilinear uniformly accelerated motion of a point. They are straight lines parallel to the abscissa axis: a x = const. Graphs 1 and 2 correspond to movement when the acceleration vector is directed along the OX axis, graph 3 - when the acceleration vector is directed in the opposite direction to the OX axis.

With uniformly accelerated motion, the velocity projection depends linearly on time: υ x = υ 0x + a x t. Figure 1.34 shows graphs of this dependence for these three cases. In this case, the initial speed of the point is the same. Let's analyze this graph.

Projection of acceleration From the graph it is clear that the greater the acceleration of a point, the greater the angle of inclination of the straight line to the t axis and, accordingly, the greater the tangent of the angle of inclination, which determines the value of the acceleration.

Over the same period of time, with different accelerations, the speed changes to different values.

With a positive value of the acceleration projection for the same period of time, the velocity projection in case 2 increases 2 times faster than in case 1. With a negative value of the acceleration projection on the OX axis, the velocity projection modulo changes to the same value as in case 1, but the speed decreases.

For cases 1 and 3, the graphs of the velocity modulus versus time will be the same (Fig. 1.35).

Using the graph of speed versus time (Figure 1.36), we find the change in the coordinates of the point. This change is numerically equal to the area of ​​the shaded trapezoid, in this case the change in coordinate in 4 s Δx = 16 m.

We found a change in coordinates. If you need to find the coordinate of a point, then you need to add its initial value to the found number. Let at the initial moment of time x 0 = 2 m, then the value of the coordinate of the point at a given moment of time equal to 4 s is equal to 18 m. In this case, the displacement module is equal to the path traveled by the point, or the change in its coordinate, i.e. 16 m .

If the movement is uniformly slow, then the point during the selected time interval can stop and begin to move in the direction opposite to the initial one. Figure 1.37 shows the dependence of the velocity projection on time for such a movement. We see that at a time equal to 2 s, the direction of the velocity changes. The change in coordinate will be numerically equal to the algebraic sum of the areas of the shaded triangles.

Calculating these areas, we see that the change in coordinate is -6 m, which means that in the direction opposite to the OX axis, the point has traveled a greater distance than in the direction of this axis.

Square above we take the t axis with a plus sign, and the area under the t axis, where the velocity projection is negative, with a minus sign.

If at the initial moment of time the speed of a certain point was equal to 2 m/s, then its coordinate at the moment of time equal to 6 s is equal to -4 m. The modulus of displacement of the point in this case is also equal to 6 m - the modulus of change in coordinates. However, the path traveled by this point is equal to 10 m - the sum of the areas of the shaded triangles shown in Figure 1.38.

Let's plot the dependence of the x coordinate of a point on time. According to one of the formulas (1.14), the curve of coordinate versus time - x(t) - is a parabola.

If the point moves at a speed, the graph of which versus time is shown in Figure 1.36, then the branches of the parabola are directed upward, since a x > 0 (Figure 1.39). From this graph we can determine the coordinate of the point, as well as the speed at any time. So, at a time equal to 4 s, the coordinate of the point is 18 m.

For the initial moment of time, drawing a tangent to the curve at point A, we determine the tangent of the angle of inclination α 1, which is numerically equal to the initial speed, i.e. 2 m/s.

To determine the speed at point B, draw a tangent to the parabola at this point and determine the tangent of the angle α 2. It is equal to 6, therefore the speed is 6 m/s.

The graph of the path versus time is the same parabola, but drawn from the origin (Fig. 1.40). We see that the path continuously increases over time, the movement occurs in one direction.

If the point moves at a speed, the graph of the projection of which versus time is shown in Figure 1.37, then the branches of the parabola are directed downward, since a x< 0 (рис. 1.41). При этом моменту времени, равному 2 с, соответствует вершина параболы. Касательная в точке В параллельна оси t, угол наклона касательной к этой оси равен нулю, и скорость также равна нулю. До этого момента времени тангенс угла наклона касательной уменьшался, но был положителен, движение точки происходило в направлении оси ОХ.

Starting from the moment of time t = 2 s, the tangent of the angle of inclination becomes negative, and its module increases, this means that the point moves in the direction opposite to the initial one, while the module of the movement speed increases.

The displacement module is equal to the module of the difference between the coordinates of the point at the final and initial moments of time and is equal to 6 m.

The graph of the distance traveled by a point versus time, shown in Figure 1.42, differs from the graph of displacement versus time (see Figure 1.41).

Regardless of the direction of the speed, the path traveled by the point continuously increases.

Let us derive the dependence of the point coordinates on the velocity projection. Speed ​​υx = υ 0x + a x t, hence

In the case of x 0 = 0 and x > 0 and υ x > υ 0x, the graph of the coordinate versus speed is a parabola (Fig. 1.43).

In this case, the greater the acceleration, the less steep the branch of the parabola will be. This is easy to explain, since the greater the acceleration, the less the distance that the point must travel for the speed to increase by the same amount as when moving with less acceleration.

In case a x< 0 и υ 0x >0 the velocity projection will decrease. Let us rewrite equation (1.17) in the form where a = |a x |. The graph of this relationship is a parabola with branches directed downward (Fig. 1.44).

Accelerated movement.

Using graphs of the velocity projection versus time, you can determine the coordinate and acceleration projection of a point at any time for any type of movement.

Let the projection of the point's velocity depend on time as shown in Figure 1.45. It is obvious that in the time interval from 0 to t 3 the movement of the point along the X axis occurred with variable acceleration. Starting from the moment of time equal to t 3, the movement is uniform with a constant speed υ Dx. According to the graph, we see that the acceleration with which the point moved was continuously decreasing (compare the angle of inclination of the tangent at points B and C).

The change in the x coordinate of a point during time t 1 is numerically equal to the area of ​​the curvilinear trapezoid OABt 1, during time t 2 - the area OACt 2, etc. As we can see from the graph of the velocity projection versus time, we can determine the change in the coordinate of the body over any period of time.

From a graph of coordinates versus time, you can determine the value of speed at any point in time by calculating the tangent of the tangent to the curve at the point corresponding to a given point in time. From Figure 1.46 it follows that at time t 1 the velocity projection is positive. In the time interval from t 2 to t 3, the speed is zero, the body is motionless. At time t 4 the speed is also zero (the tangent to the curve at point D is parallel to the x-axis). Then the velocity projection becomes negative, the direction of motion of the point changes to the opposite.

If the graph of the velocity projection versus time is known, you can determine the acceleration of the point, and also, knowing the initial position, determine the coordinate of the body at any time, i.e., solve the main problem of kinematics. From the graph of coordinates versus time, one can determine one of the most important kinematic characteristics movement - speed. In addition, using these graphs, you can determine the type of movement along the selected axis: uniform, with constant acceleration, or movement with variable acceleration.

Labor of hired workers in various fields economic activity assumes completely different schedules for their involvement in the work process. If office workers Work, as a rule, under conditions of a five- or six-day work week, then, for example, the service sector requires a completely different regime. A schedule is drawn up for each employee, which may include night work, shifts, and “floating” days off. In the meantime, it is impossible to draw up a schedule, guided only by the own wishes of the employer and employee - there are a lot of rules that are enshrined in labor legislation.

What is a labor regime, what elements does it consist of?

Time worked is the basis for remuneration for employees with a time-based condition for payment

Labor law obliges the employer to keep strict records of working time for each employee, because it is for time (with the exception of rather rare cases of piecework) that payment for work occurs. The labor regime is determined first of all by law, and secondly by the employer in agreement with the trade union and the employee, the rules for the distribution of time. The Labor Code of the Russian Federation contains a section devoted to working time, a separate chapter of which (Chapter 16) regulates this particular regime.

Working hours according to the Labor Code of the Russian Federation can be represented by several types of duration: normal, shortened and incomplete. In addition, special varieties include night work, overtime work, and work with the possibility of irregular days. The main difference between part-time and short-time working hours is their payment - the first means payment in proportion to the hours worked, the second - regardless of the hours worked. Night and overtime work are paid at an increased rate; irregular working hours are, as a rule, compensated for by additional days of the annual vacation period.

Elements of the working time regime are those positions that, in accordance with the law, must be determined when forming a regime for each worker. Among these main positions, the Labor Code of the Russian Federation names:

• duration (number of working days) of the week (for example, five-day or six-day, incomplete, indicating the number of days, etc.);
• the presence of a condition on irregular working hours;
• duration of daily work - number of hours working day or shifts with an exact indication of their beginning and end, time frames for breaks;
• number of shifts per day;
• rules for alternating working and free days (for example, “two working days after two days off”, etc.).

How and by what documents the labor regime is determined

The work schedule for each individual employee must be discussed with him in advance - when concluding an employment agreement. In general, according to the organization in the context of structural divisions or positions, the working hours are determined in the internal labor regulations.

PVTR is a local regulatory legal act of an organization that defines the main aspects of the relationship between a team of employees and the employer - rules for hiring and termination labor relations, powers and obligations of the parties to the employment agreement in the process of work, General terms regarding the working time regime, etc. PVTR are approved by the employer in agreement with the trade union organization; each employee must be familiarized with this document in writing when concluding an employment contract.

In the PVTR, the working time regime of an organization can be reflected by:

• establishing the duration of the work week and specific daily work time frames for certain groups of positions (for example, “For departments: Management, Human Resources Department, Legal Service, Accounting, Office - a five-day work week, the beginning of the working day is 8:00, the end of the working day day - 17:00, break for rest and food - from 13:00 to 14:00");
• establishing for certain positions the condition of an irregular working day, indicating the amount of compensation in the form of additional days (at least three) of vacation in accordance with Art. 119 of the Labor Code of the Russian Federation (for example, “For positions: Director, Deputy Director, driver - an irregular working day is established with compensation in the form of 4 days of additional vacation period annually”);
• establishing a work schedule for individual departments and positions (for example, “For the sales department, a work schedule is established in compliance with labor standards for a five-day, 40-hour work week”);
• establishing a summarized accounting of working time for individual positions (for example, “For the position “Seller”, a summarized accounting of working time is established, the accounting period is a quarter”);
• establishing flexible schedule work, night (equated to daytime) work schedule, shift schedule, division of the working day into parts for certain categories of workers (for example, “For the position “Cashier” it is established shift work work, in which the third shift, falling at night, is equivalent to daytime working hours").

The employment agreement must contain a section dedicated to the working regime. For employees whose position involves working a regular schedule of five or six days a week, the agreement specifies the exact work schedule. For those who will work according to a schedule, with cumulative accounting, with irregular working hours, with incomplete working time, with the division of the day into parts, etc. these circumstances must be reflected in the specified agreement. Cases of establishing an unspecified working time regime are illegal; such a violation may entail liability for the employer under Art. 5.27 of the Code of Administrative Offenses of the Russian Federation with all the ensuing consequences (fines and other sanctions).

A section on working hours must be included in the contract

How to establish new regime rules in an organization: procedure and documents

If an employee becomes familiar with the existing regime for a particular position when being hired by signing an employment agreement and marking the reading of the PVTR, then changing the current regime is somewhat more complicated.

The decision to change the PVTR can be issued in the form of an order

The procedure is as follows:

1. To begin with, the manager must make an informed decision about for which positions or structural units new rules are being introduced.
2. Then, in accordance with all the rules for changing the local regulatory legal acts, the corresponding changes are made to the PVTR (the project must be agreed upon with the trade union within five days, then signed by the manager).
3. Based on the amended PVTR, each employee affected by the changes is warned of changes in essential working conditions (notice must be handed in against signature no later than a month before the order is issued). In case of refusal to continue the employment relationship under the changed conditions, the employee must be dismissed upon expiration of the notice period.
4. IN fixed time(a month after notifying employees), an order is issued for the enterprise to change the regime for specific employees (at this stage they must be listed by name). Each employee gets acquainted with the order by signing it.
5. On the day of publication administrative document An additional agreement to the contract is concluded with each employee, changing the terms of the working time regime.
6. Begins to be effective from the date specified in the additional agreement and order new mode with its new documentary design (for example, with drawing up schedules).

Work schedule as a document regulating daily individual work schedule

Work schedule is one of important documents to organize the work of those employees who do not work according to the general (production) calendar. Thus, the daily schedule regulates the time of coming to work, leaving work, break times, and even the workplace assigned to the employee.

The schedule is usually drawn up for one month, however, this period is not regulated by law. Therefore, depending on the circumstances and characteristics production process the document can be drawn up for a week, a quarter, or a year.

The schedule, as a document, can be drawn up:

• simultaneously for all employees of the enterprise;
• per employees of one structural unit;
• for a certain group of employees from different structural divisions;
• separately for one employee.

Form and symbols

In the shift schedule it is enough to indicate only the shift designation

When summarizing accounting, the schedule must contain columns reflecting the amount of hours per month, per quarter (depending on the accounting period)

The process of drawing up and approving the schedule

The procedure for drawing up and approving a schedule in an organization can be regulated either by a local regulatory legal act or by order of the manager. Persons responsible for maintaining, approving and approving documents are determined by designation in these documents and the inclusion of a corresponding item in the job description.

As a rule, the schedule is drawn up by the person responsible for this in the structural unit (department, service), endorsed by the head of the structural unit, a representative of the personnel department and the trade union, approved by the head of the enterprise or his deputy in charge of the relevant area of ​​activity.

The schedule can be drawn up either manually (using standard Office tools with output on paper) or in specialized software systems(for example, “1C: Personnel and Salary”, SAP, etc.).

Schedule requirements

When drawing up a work schedule, the employer is in a situation where it is necessary to comply with a lot of rules, requirements and interests. First of all, these are the requirements labor legislation, protecting the rights, interests and even health of the employee:

1. The duration of daily work should not exceed those established by Art. 94 of the Labor Code of the Russian Federation limits (special limits are established for minor employees, disabled people, workers in harmful unsafe conditions).
2. Number working hours per week should not exceed the norm according to the production calendar (40 hours - according to general rule). For those who have been assigned summarized accounting for an accounting period, it is imperative to comply with the standard hours for this accounting period (quarter, month, etc.).
3. Shifts that primarily occur at night should be reduced by 1 hour.
4. After a shift lasting more than 24 hours, an equal or greater rest period is provided.
5. If the employee does not have a condition for dividing the working day into parts, his lunch break (or the sum of several during the day) should not last more than two hours.
6. The minimum lunch break is 30 minutes. It is obligatory to establish daily, if the agreement of the parties and the PVTR does not provide for the employee to eat food in parallel with work. Lunch break is not paid.
7. It is prohibited to work during two shifts following one another.
8. Hours that fall during an employee's illness or vacation are also included in his monthly (quarterly) rate. In other words, the employee is not required to make up the hours actually missed to normal.
9. The limits established by Art. 99 Labor Code of the Russian Federation for overtime work(no more than four hours in a two-day working period, no more than one hundred and twenty hours per year), etc.

Of course, when creating a schedule, the operating mode of the enterprise, workload standards, and the interests of the employee himself are taken into account.

Employee familiarization

The employer is obliged to familiarize employees with the work schedule no later than one month before the day it comes into effect - this is a direct requirement of Art. 103 Labor Code of the Russian Federation. Violation of this deadline may result in administrative liability.

To avoid violating the requirements of the law, you should start drawing up a schedule no later than one and a half months before the start of the accounting period. For example, the schedule for December should be drawn up before October 15 in order to have time to coordinate, approve and familiarize all employees with it (after all, some of them at the time of familiarization may be on vacation or on sick leave, but this circumstance is not an excuse in case of violation of the deadlines for familiarization ).

How to change the established work schedule

Since the work schedule is established by agreement of both parties to the labor relationship, any of them can initiate its change. Changing the regime (as a more general, permanent concept) on the initiative of the employer is described in the section on establishing a labor regime at the enterprise. A change in the schedule, as a one-time event or an incident affecting one employee, occurs:

• or by adjusting an already drawn up schedule (document), if a work schedule has been established for the employee;
• or by making changes to contract of employment- if the employee works according to the schedule recorded in this document (that is, according to the normal production calendar).

In the first case, the scheduler, at the request of the employee or on his own initiative (due to production needs), draws up a corrective schedule, endorses and approves it according to the usual procedure for preparing this document.

You can change the working hours either for a group of employees or for one of them (for example, at his request due to family circumstances)

In the second case, at the request of the employee, an order is prepared to change the work schedule - this is enough if the schedule changes for up to two weeks. If the period of change in the working regime is longer, it is necessary to conclude an additional agreement to the contract.

If the work schedule changes for more than two weeks, it is necessary to conclude an additional agreement to the employment contract

Establishing work hours and drawing up schedules for workers is one of the employer’s primary tasks in organizing the labor process. And this is not an easy matter. The schedule must correspond not only to the production needs of the company, but also to the conditions defined by the legislator. In addition, it is extremely important to familiarize employees with the schedule in a timely manner in order to avoid possible sanctions from government agencies exercising control in the field of labor relations.

I have a higher legal education, experience working in court, a bank, and an enterprise. Despite the fact that my main specialization is criminal law and procedure, my entire professional activity associated with commercial law, ranging from personnel issues and ending with credit problems. For a long time I have been writing reviews of foreign and domestic media on business topics.

Estrogen-progesterone deficiency b

If the temperature in the second phase does not rise either independently, or with prayers, or with the persuasion of girlfriends, if the difference in temperature in phases 1 and 2 is no more than 0.2–0.3°, this may indicate estrogen-progesterone deficiency.

Estrogen deficiency

If the basal temperature jumps like a March hare, large temperature swings are noticeable - this means that the woman may have estrogen deficiency. A qualified gynecologist should simply require tests for hormones, an ultrasound examination, and only after such manipulations prescribe medications.

Hyperprolactinemia

The hormone prolactin is known to be responsible for pregnancy. Due to the increase in this hormone (the body seriously thinks that you are pregnant), the basal temperature graph may be similar to the graph of a pregnant woman. Menstruation, just like during pregnancy, may not occur.

Inflammation of the appendages

Another reason for the rise in temperature in the first phase is inflammation of the appendages. Then the temperature rises only for a few days to 37 degrees, after which it drops again. This is difficult in these graphs because the increase masks the ovulatory rise.
In the first phase of the cycle, the temperature from days 11 to 15 stays at 37 degrees, the rise occurs sharply and drops sharply. An increase in temperature on the 9th day can be mistaken for an ovulatory rise, but in fact it is more likely to indicate inflammation. Therefore, it is very important to measure the temperature throughout the entire cycle in order to exclude a similar scenario: the temperature rose as a result of inflammation, then fell again, then rose due to ovulation.

Endometritis

The temperature in the first phase should normally decrease with menstrual bleeding. If a woman’s temperature at the end of the menstrual cycle drops before menstruation and rises again to 37 degrees after the start of menstruation, this may indicate the presence of endometritis. A characteristic feature is a drop in temperature before menstruation and an increase with the beginning of another cycle. If there is no drop in temperature before menstruation in the first cycle, that is, the temperature remains at this level, pregnancy can be assumed, despite the bleeding that has begun. You should take a pregnancy test and contact a gynecologist who will perform an ultrasound to make a diagnosis.