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STRAIGHT ROH- ruh, for which the displacement vector does not change directly and according to the size of the longest road passed by the body. RIVNOMIRNY STRAIGHT-LINE ROH- Ruh, with such a body for equal intervals, the hour is the same moving. Shvidkіst with equal rectilinear Russian is fast: v=const. RIVNOMIRNIY I NERIVNOMIRNIY STRAIGHT-LINE ROHRivnomirny Rukh- Ruh, with such a body, for the same time, for the same time, the same movement (Earth, planets, escalator, arrow of the year). The speed of equal movement- a physical quantity that characterizes the path, the passage of the body in one hour. The uneven movement is characterized by an average and mitt swidkistyu. Medium swedishness- Tse that security, with which body in the middle it is given to pass. Won dobrіvnyuє vodnoshnyuє vіdnoshnyu vsogo movіshchennya till promіzhku hour, protyago tse tse miіshchennya passed. v=S/t v - speed S - stand up t - Hour Mitteva shvidkist- Tse shvidkіst at a given moment to an hour or at a given point of the trajectory. It’s a good idea to make a small move to make a small interval for an hour, by stretching such a move for a short time. Equivalent Rukh- Ruh, when the speed of the body changes for equal time by the same value. priskorennya- Physical quantity that characterizes the speed of change of speed. |
STRAIGHT ROH- ruh, in case of which the displacement vector does not change in a straight line and according to the value of the longest path passed by the body. RIVNOMIRNE STRAIGHT RUH- ruh, with such a body for equal intervals, the hour is equal to the same movement. Shvidkіst with equal rectilinear Russian is fast: v=const. RIVNOMIRNIY I NERIVNOMIRNIY STRAIGHT-LINE ROHRivnomirny Rukh- Rukh, with such a body, for the same time, for the same time, the same movement (Earth, planets, escalator, arrow of the yearbook). The speed of equal movement- a physical quantity that characterizes the way, the passage of the body for a single year. The uneven movement is characterized by an average and mitt swidkistyu. Medium swedishness- tse shvidkіst, with such a body in the middle to pass tse vіdstan. It’s a good day for the entire relocation until the next year, for which the relocation has been completed. v=S/t v - Shvidkist S - Vіdstan t - year Mitteva shvidkist- tse speed at a given moment of the year or at a given point of the trajectory. It’s a good idea to make a small move to a fairly small interval of a year, for which the move is cheap. Equally perervny Rukh- ruh, with a change in the speed of the body for equal periods of time, it changes by one and the same value. priskorennya- a physical quantity that characterizes the firmness of the change in firmness. |
manager
Three points A and B nazustrich, one to one, a motorcyclist and a cyclist swayed at the same time. The stench was on the road 4 km from B, and at the moment the motorcyclist arrived at point B, the cyclist was on the road 15 km from A. Know the road between A and B.Solution.
Move between points A and B become time
Obviously, at the time of t 1 at the distance of 4 km, the motorcyclist will pass 4 km less, lower distance from A to B.
S - 4 = v 1 t 1
t 1 \u003d (S - 4) / v 1
A cyclist travels 4 km in one hour to
4 = v 2 t 1
t 1 \u003d 4 / v 2
Oskіlki hour, scho proyshov to zustrіchі one and the same, tobto dorivnyuє t 1,
(S - 4) / v 1 = 4 / v 2
Now we can see the motorcyclist's security through the cyclist's security
4v 1 = v 2 (S - 4)
v 1 \u003d v 2 (S - 4) / 4
Let's look at a friend's task. In an hour, after passing the first run, the motorcyclist managed to cover 4 km,
Let's put it on the equal speed of a motorcyclist, I can see it through the speed of a cyclist, we take it
4 \u003d v 2 (S - 4) / 4 * t 2
The cyclist at this hour was 15 km from A, having passed 19 km less (15 + 4), lower from A to B. He did not reach 15 km from V, and at the moment of the frontal zest, he already knew for chotiri kilometers from B. Meaning for the whole hour passed, it turns out to be equal:
S - 19 \u003d v 2 t 2
Oskіlki hour, which past insults - those same, significant yoga for a motorcyclist like:
T 2 \u003d 16 / (v 2 (S - 4))
But for a cyclist
T 2 \u003d (S - 19) / v 2
Oskіlki hour - one and the same
16 / (v 2 (S - 4)) = (S - 19) / v 2
And now let's multiply the left and right part by v 2:
16/(S - 4) = S - 19
Rozv'yazhemo otrimane equal:
(S - 4) (S - 19) = 16
S 2 - 4S -19S + 76 - 16 \u003d 0
S 2 - 23S + 60 = 0
D=289
x 1 = 20
x 2 \u003d 2.5 (not satisfied with the minds of the task)
Vidpovid: 20 km
manager
For 2 years the steamboat collapsed like a river in the fog. after that, as the fog rose, the steamboat udvіchі zbіlshiv swidkіst i pliv shche 6asіv. What is the path through the fog, what is the average speed for 8 years of sailing 14 km / year?Solution.
The average speed is more than a day passed until one o'clock, for which the won was passed. Tobto
Vav = S/t
For our vipadu
Vav = (S 1 + S 2) / (t 1 + t 2)
It is significant for the first time when the number of:
S 1 \u003d v 1 t 1
S 1 = v 1 * 2
For a different amount of quantity:
S 2 \u003d v 2 t 2
S 2 \u003d v 2 * 6
Oskіlki v 2 = v 1 * 2 then
S 2 \u003d v 1 * 2 * 6
For cob virases, Vav = (S 1 + S 2) / (t 1 + t 2) the known value is conceivable:
Vav = (v 1 * 2 + v 1 * 2 * 6) / (2 + 6)
Vav = 14v 1/8
Oskelki average speed is set for the mind, then
14=14v 1/8
stars
v 1 = 8 km/year
Vidpovid: 8 km/year
Mechanical move name the change in the position of the body of another body
System to follow name the body of the object, bind the coordinate system of that year with it.
Tіlom vіdlіku naming a body, which one looks at the camp of other bodies.
material point name the body, the names of which in this task can be defied.
trajectory name a clear line, as if describing a material point for one's own Russia.
For the form of the trajectory, the ruh is divided into:
a) straightforward- trajectory along the straight line;
b) curvilinear- Trajectory є vіdrіzok curves.
way- tse dozhina traektorії, yaku vyznaє material point for the whole hour. Ce is a scalar quantity.
Relocation- tse vector, which connects the post camp of the material point with the end camp (div. Fig.).
It is even more important to understand which way is winding up in the course of moving. The most important authority for those who moved is the vector with the cob at the point of direction and with the end at the point of recognition (for which it is absolutely unimportant, by which route the movement was carried). And the way - tse, dial, scalar value, which reflects the length of the trajectory passed.
Rivnomirnim rectilinear move naming a move, with which a material point for whether or not it is equal to the hour of the same movement
Shvidkіstyu equal rectilinear movement name the transfer date until the hour, for which the transfer was made:
For the nerіvnomіrnogo Rukh koristuyutsya understand medium crispness. Often enter the average speed as a scalar value. The price of the speed of such an even rіvnomіrny rukh, with such a body to go through the same path for the same hour, which is for the uneven rukh:
Mitteva shvidkistya name the speed of the body at this point of the trajectory of the hour at a given moment.
Equal acceleration rectilinear movement- ce rectilinear ruh, with some mitteva swidkіst for whether or not equal intervals change by the same amount
The location of the coordinates of the body per hour in equal straight-line Russia may look like: x = x 0 + V x t, de x 0 – postal coordinate of the body, V x – speed of the hand.
Free fall call equal accretions ruh from fast accretions g = 9.8 m/s2, scho not to lie in the mass of the falling body. It will seem less like a surge of gravity.
Security in case of a free fall is insured according to the formula:
Moving vertically is covered by the following formula:
One of the sights of the movement of the material point is the movement of the stake. With such a Russian, the swidth of the body is straightened by a dotted one, drawn to the stake at that point, where the body is known (linear swidkist). It is possible to describe the position of the body on the stake using an additional radius drawn from the center of the stake to the body. The movement of the body under the hour of the turn along the stake is described by turning the radius of the stake, which brings the center of the stake with the body. The setting of the radius of the turn to the interval of the hour, the stretch of which turn becomes, characterizes the speed of the movement of the body along the stake and ring kutovy shvidkosti ω:
Kutova swidkіst pov'azana s line swidkіst spіvvіdshennyam
where r is the radius of the stake.
The hour, by which the body describes the next turnover, is called the period of the beast. The value, zvorotna to the period - the frequency of obіgu - ν
Oskіlki in equal Russia, according to the stake, the modulus of speed does not change, but changes directly in speed, in such Russia it is accelerated. Yogo name to the center of the roots, It is directed along the radius to the center of the stake:
Basic concepts and laws of dynamics
Part of the mechanics that caused the cause, that caused the accelerated body, is called dynamics
Newton's first law:
Establish such a system in vidlіku, schodo such a body saves its security permanently or rests, yakscho on a new one does not develop other bodies or compensates for other bodies.
The power of the body to save the camp is calm, but equal rectilinear flurry with the vrіvnovazheniye zvnіshnіh forces, which act on the new one, is called inertia. The manifestation of the preservation of the body's mobility in the presence of strong forces is called inertia. Inertial systems to look at to name the systems, in which Newton's first law is victorious.
Galileo's principle of visibility:
override in all inertial systems due to the same cob minds, all mechanical phenomena proceed the same way, that is. conform to the same laws
Masa- the world's inertia body
Force- tse kіlkіsna of the world vzaєmodії tel.
Newton's other law:
The strength, which is on the body, is good for the recovery of the mass of the body on the quick, which is supported by strength:
$F↖(→) = m⋅a↖(→)$
The stacking of forces is used by the knowing equal number of forces, so that they can cope with the same task, like a sprat at once of the forces.
Newton's third law:
Forces, with which two bodies work one on one, are spread on one straight line, equal behind the module and parallel behind the straight line:
$F_1↖(→) = -F_2↖(→) $
III Newton's law substantiates that, having poured bodies into each other, have the character of mutual modality. Yakshcho tіlo A dіє tіlo B, those tіlo B dіє tіlo A (div. fig.).
Abo is shorter, the strength of others is stronger than the forces of opposition. Nutrition is often blamed: why throw the sled, if the bodies interact with equal forces? It's better if the rahunoks are mutually compatible with the third body - the Earth. The force that hoards vpirayutsya into the ground, may be greater, lower force rubbing the sleigh on the ground. Otherwise, the hoard will be licked, and the stone will not be destroyed from the month.
If the body gives rise to deformation, then the forces that overcome this deformation are blamed. Such forces are called spring forces.
Hooke's law write down at a glance
where k is the stiffness of the spring, x is the deformation of the body. The sign "−" indicates that the strength of that deformation is straightened at the side of the cut.
In Russia, there are forces alone that forces are showing up to change the pace. Qi forces are called rubbing with strength. Razrіznyayut rubbing calm that tertya forging. Strength rubbing forging take care of the formula
de N is the reaction force of the support, µ is the coefficient of friction.
Tsya strength does not lie in the area of tertovikh bodies. The coefficient of loss is to fall into the type of material, from such a crushing of the body, that as the quality of the processing of their surfaces.
Rubbing calm blame, because the body does not move one at a time. The strength of losing calm can change from zero to a singing maximum value.
gravitational forces naming forces, as if two bodies are attracted one to one.
Law of all-world gravity:whether two bodies are attracted one to one with a force directly proportional to the gain of their mass and wrapped in a proportional square between them.
Here R - stand between the bodies. The law of all-world gravity in such a look is fair either for material points, or for bodies of a splendid form.
Vaga tila name the force, with such a body embossing on a horizontal support that stretches the suspension.
Gravity force- tse force, with which all bodies are attracted to the Earth:
With a firm support of the body, the body is supported behind the module by the force of gravity:
As if the body is collapsing vertically due to acceleration, yoga vaga will change.
In Russia, the body is quickened, we straighten the mountain, yoga vaga
It can be seen that the body of the body is larger than the body of the body that is resting.
In Russia, the body is quickened, straightened down, yogo vaga
In this way, the body of the body is less than the body of the body that is resting.
Nevagomistu such a rot of the body is called, for which yogi has an accelerated death, tobto. a = g. It is possible in that moment, as there is only one force on the body - the force of gravity.
Piece satellite of the Earth- all the body that V1 is capable of, enough for it to collapse on a stake near the Earth
There is only one force on the satellite of the Earth - the force of gravity, directed to the center of the Earth
First space swede- tse shvidkіst, yak treba povіdomiti tіlu, schob it turned around the planet in a circular orbit.
de R - walk through the center of the planet to the satellite.
For the Earth, near the її surface, the first space flight
1.3. Basic concepts and laws of statics and hydrostatics
The body (material point) is resting at the station of the river, as if the vector sum of forces, which work on the new, reaches zero. There are 3 types of jealousy: stіyke, nestіyke and baiduzhe. Like when the body is seen from the position of the equal, forces are blamed, like to move, turn the whole body back, stіyka rіvnovaga. How to blame the forces, how to pragnate in the body more far away from the jealousy, non-stationary camp; if you don’t blame the human forces - baiduzhe(Div. Fig. 3).
If it is not about the material point, but about the body, as if all wrappings are possible, then in order to achieve the position of equalness of the crim equal to zero, the sum of forces that work on the body, it is necessary, that the algebraic sum of the moments of all forces that work on the body, reached zero.
Here is the d-shoulder of the force. Shoulder of strength d name the distance from the axis of wrapping to the line of force.
Umova jealously important:
the algebraic sum of the moments of all forces that wrap the body is equal to zero.
Tiskom name the physical quantity, which is the most important extension of the force, which is directed to the Maidanchik, perpendicular to this force, to the square of the Maidanchik:
For home and gas fair Pascal's law:
The pressure is expanding in all directions without change.
If the homeland, or gas, is in the field of gravity, then the leather vyscherozashovaniya ball is embossed on the lowerstashovanі, and in the world it is zanurennya in the middle of the rodiny, but the pressure of the gas is growing. For natives
de ρ - thickness of the rіdini, h - depth of penetration into the rіdina.
A homogeneous motherland in successful ships is established on the same equal footing. If a number of successful ships flood the motherland with different heights, then the motherland with a greater strength will be restored to a lower height. In what direction
The heights of the heights of the middle are wrapped in proportion to the widths:
Hydraulic press is a vessel, filled with oil or another motherland, in a pierced hole open two, closed with pistons. Pistons wash the area. If you apply force to one piston, then the force applied to the other piston appears differently.
In such a rank, the hydraulic press serves as a transformation of the magnitude of force. If the pressure under the pistons can be the same, then 
Todi A1 = A2.
On the body, zanurene in the homeland, or gas, from the side of the cієї rіdini, or the gas, the power is straightened uphill vishtovhuvalna, how to call by the power of Archimedes
The magnitude of the force that vishtovhuє, install law of Archimedes: on the body, zanurene in the homeland or gas, strong vishtovhuvalna force, straightened vertically uphill and dovnyuє vazi rіdini or gas, covered with body:
de ρ rіdk - shіlnіst rіdini, in a yak zanurené body; V burial - obsyag burried part of the body.
Umova swimming pool- The body floats in the countryside or gas, if the vishtovhuval strength is on the body, the strength of gravity is stronger, it is on the body.
1.4. Save money
body impulse name the physical value, equal to the additional weight of the body on yoga swidkist:Impulse is a vector quantity. [p] = kgm/s. The order of the body impulse often coryst force impulse. Tse vitvir force for an hour її dії
Changing the impulse of the body is more important to the impulse of the dignified body of strength. For an isolated system tіl (system, tіla that vzaimodiyut only one with one) law of conservation of impulse: the sum of the impulses of the air of the isolated system until the intermodality is equal to the sum of the impulses of the air after the intermodality.
mechanical robot name the physical quantity, as a result of the increase in strength, which is on the body, on the displacement of the body, and on the cosine of the cut between the direct force and displacement:
Tension- tse robot, vikonan at one hour:
The building of the body is to be characterized by the size of the robot, how to name it energy. Divide mechanical energy into kinetic and potential. How can the body win over the robot for the sake of its rahu, it seems that it can kinetic energy. The kinetic energy of the progressive movement of the material point is supported by the formula
How can the body be beaten by the robot for the account of changing its position to other bodies, or for the account of changing the position of parts of the body, there may be potential energy. The butt of potential energy: the body that is lifted above the ground, this energy is boosted by the formula
de h - height pidyom
Energy of compressed spring:
de k – spring hardness coefficient, x – absolute deformation of the spring.
The amount of potential and kinetic energy to become mechanical energy. For the isolated system tіl at the mechanics of justice law of conservation of mechanical energy: even though the bodies of the insulated system do not lose strength (otherwise, the forces that produce up to a rise in energy), then the sum of the mechanical energies of the system does not change (the law of conservation of energy in mechanics). As if the forces were rubbing between the bodies of the insulated system, then when interacting, a part of the mechanical energy of the body would pass to the internal energy.
1.5. Mechanical chiselling and whil
colivans Rukhs are called, which make that chi and the next step of repetition in the hour. Collivans are called periodic, as the values of physical quantities that change during the colonization process are repeated every other hour.Harmonious colivans such colivanya are called, in some physical quantity x, which is kolivaetsya, changes according to the law of sine or cosine, that is.
The value A, which is equal to the largest absolute value of the physical quantity x, which is called, is called amplitude. Viraz α \u003d ωt + ϕ indicates the value of x at a given moment and is called the colivan phase. Period T the hour is called, for the sake of the body, which is important, it is the same outside of the colivanya. The frequency of periodic knocks name the number of new kolivans, knocked down in one hour:
The frequency is reduced to s-1. This unit is called hertz (Hz).
Mathematical pendulum a material point is called with a mass m, suspended on a non-vagomic non-stretching thread and repairing a buckling near a vertical plane.
As soon as one end of the spring is closed firmly, and until the next end, attach the body to the mass m, then when the body is removed from the equal position, the spring will be stretched and the body will be knocked out on the springs in the horizontal or vertical plane. Such a pendulum is called a spring pendulum.
Koliva period of the mathematical pendulum follow the formula 
de l - pendulum dove.
Period of colivan vantage on springs follow the formula 
de k - hardness of the spring, m - mass vantage.
Widening of the colivan at the spring centers.
The middle is called springy, as if between the particles, there are forces of mutual modality. Whilst is called the process of expanding the colivan in springy middles.
Khvilya is called transverse, so that the particles of the middle part are collapsing at straight lines, perpendicular to the straight line widening of the hairs. Khvilya is called late, Yakshcho kolyvannya particles of the middle of the heart in the direct expansion of the whil.
Longevity's wind are called between the two nearest points, which are in the same phase:
de v - swidkіst widening whvili.
With sonic whistles call the winds, the colivannya in some of them are known from frequencies like 20 to 20,000 Hz.
Shvidkіst sound is different in different middles. The speed of the sound again becomes 340 m/s.
Ultrasonic waves call whil, the frequency of colivans among them is 20,000 Hz. Ultrasound waves are not perceived by human breath.
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Lesson 3 For example, the car rushes to chi galmuє. Let at the moment of the hour the body was at the point with the coordinate, and at the moment of the hour + at the point with the coordinate +Δ (div. Fig.). r + Δ X The average value of the projection of the smoothness of the point in the interval up to If you now look at a smaller interval of an hour, then the movement of the body will also be smaller for the module, and the remembrance of the mother will be even more important. As soon as we let the hour change, then the value of the average speed for that gap practically ceases to change. Otrimana value є mittevoy projection of the body's fluidity at the moment of the hour. At the same time, you can change as a module, and directly as a speed vector. For example, the speed of a stone thrown under a deaky kut to the horizon changes like a module, and straight ahead. A υ r cf r s r B B At the moment of the hour, the body is at point A, and at the moment + at point B. We know the average firmness of the body in the interval from to +, vicorist is assigned: r s r por_vn. The direction of the vector r cf is shifted from the direction of the displacement vector s r. Now zimshuvimatimo magnitude, with the central module of the vexeshnna vector, I will become Zhanshuvatsya, and thwise clogged to a dotto's dotties directly to the tractorі. often її simply called swidkistyu) is straightened along the dotique to the trajectory at this point. Mitteva speed is a vector quantity, which is more expensive to move the body Δ s r to the interval of an hour, stretching out some kind of movement, when exercising: r Δ s r Δ
2 Equally variable movement The simplest kind of uneven movement is an evenly alternating movement, such a movement of the body, despite the fact that the body’s swirlness changes for an hour, however, evenly. Rosemary, which characterizes the speed of the change of speed, is called the quickening. The quickening of a variable speed is a vector quantity, which is a good way to change the speed until the hour, by stretching some kind of change, it was: r a Δ r If the stench stinks straight ahead (r a r), then ruh equal improvements. Even though the early moment the body’s quickness increased r, then for the purpose of the accelerated body’s quickness at the moment the body’s quickness increased r r + a r. With a rectilinear equal Russian, the projection of the speed is constant, and the coordinate of the point is linear: +. The graph of the function () is a horizontal line (div. Fig.). Changing the coordinates of the body for the interval between one hour and the next s Δ, so that the area of the shaded rectangle is numerically improved. It is important that the change of the coordinates and the projection of the movement of the body: Δ s. In a time of equal-variable fluctuations, the projection of the thinness of the body is linearly deposited at the hour: () + a de ce projection of the cob swidness on the whole X, and the projection of the quickened on the qiu of the whole (div. Fig.). Having looked at such a small interval of an hour, with a stretch of some kind of swedishness you can take in fast. Changing the coordinates of the body for the entire interval is numerically more important than the area of the white rectangle in the figure. If you break the hour for a lot of space, then the change of coordinates for the whole hour will appear numerically equal to the sum of the area of the great number of rectangles. Tsya sum with the expansion of more and more space in the area S of the shaded trapezoid OABS: S (OA + BC) OC /. Todi + Δ
3 B A + + a a Oskilki () + a, then Δ +. Tsya formula is shown for vipadku, if >, a >, prote is valid for sufficient signs of values, a. In this way, the fall of the coordinate in the hour (the law of movement) is removed: a++ The coordinate of the point to lie in the hour is not linear, but according to the quadratic law. The fallow graph () is a parabola. Like a >, then the pins of the parabola are straight up the mountain, like a< то вниз. Проекция средней скорости тела при равнопеременном движении s + ср равна среднему арифметическому начальной и конечной проекции скорости. При решении многих задач полезна формула для перемещения, не содержащая времени в явном виде. Из зависимости проекции скорости от времени () + a выразим время a и подставим в выражение для s: s Δ + C Задача. Двигаясь равноускоренно, за восьмую секунду после начала движения тело прошло путь s 5 м. Найдите время, за которое тело прошло путь l 9 м. Решение. Обозначим ускорение тела через a, а промежуток времени в секунду через. Так как начальная скорость тела равна нулю, то за время c тело прошло путь L 7 a, а за время тело прошло путь L 8 a(7 +). Тогда путь за 8-ую секунду равен a a s L 8 L 7 a (7 +/), отсюда выражаем ускорение тела: s a м/c. Δ (7 +) Путь l тело преодолеет за время, такое что l a, тогда искомое время l a 3 с.
4 Graphs of the day A graph of the fallowness of the projection of the accelerated material point is drawn on the little one, which collapses the axis OX, depending on the hour. Look at the graphs of the fallowness, the projection of the flow rate and the coordinates at the hour. The coordinate of the point that її shvidk_st y the cob moment is equal to zero. Find the average speed and the average speed of a point for the whole hour of traffic. a, m/s 34, c Significantly after, 3 and 4 moments in an hour, which means s, s, 3 s and 4 s on the cob. With a stretch of the first second and a ruh body of equal accelerations, a projection of acceleration a m / s. The speed changes according to the linear law: a, for example, the first second and m / s. The coordinate changes according to the law a/, the graph of the function () is the parabola plot with the vertex, which shows, at, the coordinate in the last second, 5 m. On the fallow graph () such a plot is depicted by a horizontal line. The coordinate changes according to the linear law: + (), for example, another second + (), 5 m. The coordinate changes according to the law +()+a()/. The graph of the function () is a parabola board with a top, which is 75 m at 5 s. At this hour, the projection of the speed of the body turns to zero, the body turns to zero, it is dotichna to the graph of the function () at this hour it is horizontal. The coordinate for example of the third second is 3.5 m. At the fourth second, the rotation of the body is equal to the velocity of 3 m/s. The coordinate changes according to the linear law: (3), for example, the fourth second (4 3.5 m). The movement of the body for the whole hour rhu n 4 s 4.5 m.
5 Task for independent vyrishennya. The body will become calm, beginning to crumble with fast graft. Know the payment for the last equal interval of an hour. Verdict: [:3:5: ].. A graph of the fallowness of the projection of the accelerated material point has been drawn on the little one, which the OX axis is collapsing at the hour. Look at the graphs of the fallowness, the projection of the flow rate, the coordinates, as well as the route passed by the point L at the hour. The coordinate of the point that її shvidk_st y the cob moment is equal to zero. Find the average speed and the average speed of a point for the whole hour of traffic. a, m/s 3 4, s
The speed of a straight straight line movement is called a vector quantity, equal to the displacement of the body to the gap.
Rivnoperemіnniy Rukh, quickened body 1. The car crashes down a straight street. The graph shows the stock of yoga stock per hour. At what interval is the car's acceleration module maximum?
Genkin B.I. Elements zmіstu, scho perevіryayutsya on ЄDI z physics. Help for repetition of initial material. St. Petersburg: hp://audioi-um.u, 1 1.1 KINEMATICS Kinematics is the science of movement. At kinematics
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Rivnoperemіnniy Rukh, quickened body 1. The car crashes down a straight street. The graph shows the amount of car's speed per hour. Why is the maximum module accelerated? Vіdpovіd vyslovіt
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Graph analysis 1. Behind the graph of the accumulation of the module of the body's fluidity at the hour, presented on the little one, in the direction of the passage of the body at the time of hour 0 to the time of hour 2 s. (Vіdpovіd give for the meter.)
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3. Control task 1 (A) Material point ce: 1) body of a small mass; 2) body more than small roses; 3) a point that shows the position of the body in space; 4) body
Rolling up the body behind a frail area (Fig. 2);
Rice. 2. Rolling the body along the thin plane ()
Vilne fall (Fig. 3).
See all the ruhu є equal, so that some change their swedishness. At this point, we can see a nervous rumble.
Rivnomirny Rukh mechanical movement, for such a body, for whether or not it is equal to the hour to pass the same day (Fig. 4).
Rice. 4. Equal movement
Rukh is called uneven, if it’s dead for equal intervals, it’s an hour to pass nerіvnі ways.
Rice. 5. Nervnomirny Rukh
The main task of mechanics is to determine the position of the body at any given moment. In the case of uneven Russia, the firmness of the body changes, and it is also necessary to learn how to describe the change in the firmness of the body. For whom, two concepts are introduced: middle swidkіst and mittєva shvidkіst.
The fact of changing the firmness of the body in uneven Russia does not need to be healed, when looking at the movement of the body at a great distance in the whole (we don’t care about the firmness of the skin at the time of the hour), it is necessary to manually introduce the understanding of the average firmness.
For example, a delegation of schoolchildren gets from Novosibirsk Sochi by train. It is about 3300 km to become between these places and the bay. The speed of the train, if only the winds from Novosibirsk became, what does it mean that in the middle of the road the speed was such and on the way to Sochi [M1]? Chi is possible, looming over qі danі, stverdzhuvati, what time we become ruhu 
(Fig. 6). Of course, the remnants of Novosibirsk city dwellers know that it is about 84 years to get to Sochi.
Rice. 6. Illustration for example
If you look at the movement of the body at the great diversity of the number as a whole, it is better to understand the average density.
Medium swedishness name a new relocation, as if the body was broken, for an hour, for a short relocation (Fig. 7).
Rice. 7. Average swidth
Don't worry about Dane's appointment. For example, an athlete runs 400 m - one colo. The movement of an athlete is good 0 (Fig. 8), but it is clear that even the average speed of zero cannot be good.
Rice. 8. Moved 0
In fact, most victorious is the understanding of the average number of swedishness.
Average road speed- tse vіdnoshnja povnogo shlyakhu, passed by the body, up to an hour, by stretching out this way is passed (Fig. 9).
Rice. 9. Middle shlyakhova shvidkіst
There is one more indication of the average speed.
Medium swedishness- this is the speed, with which the body can collapse evenly, to pass the given time for that very hour, for which it won, it passed, collapsing unevenly.
From the course of mathematics, we know what is the arithmetic mean. For numbers 10 and 36 it is more expensive:
In order to recognize the possibility of victorious formulas for the significance of the average speed, it seems to be the coming task.
manager
The cyclist rides a speed of 10 km/year on a scale, stained glass at a cost of 0.5 years. Dali zі shvidkіstyu 36 km/year descends for 10 hvilin. Find the average speed of a cyclist (Fig. 10).
Rice. 10. Illustration before the date
Given:; ; ;
Know:
Solution:
Oskіlki odinіru danih shvidkost - km / year, those and the average shvidkost know km / year. Otzhe, tsі zavdannya will not be translated into SI. Let's turn it into a yearbook.
Medium speed is good:
The last path () is folded from the path to the pidyom on the shill () and the descent from the schilu ():
The way to go to the skyl dorivnyu:
The way down the slope of the road:
An hour, for which the last path is passed, dorivnyuє:
Suggestion:.
Of course, it is impossible to calculate the arithmetic mean formula for calculating the average speed.
Do not start to understand the average speed of the correlation on the top of the head mechanics. Turning before the order about the train, it is impossible to confirm that the average speed along the entire route of the train is good, then after 5 years we will change the wine to the country 
from Novosibirsk.
The average swidkist, vymiryanu for an infinitely small interval of an hour, is called mitteva shvidkistyu body(For example: the speedometer of a car (Fig. 11) shows the speed of the vehicle).
Rice. 11. The speedometer of the car shows the speed of the vehicle
Іsnuє sche dne vyznachennya mitteva ї shvidkostі.
Mitteva shvidkist- the movement of the body at the moment of the hour, the movement of the body at this point of the trajectory (Fig. 12).
Rice. 12. Mitteva Shvidkist
To better understand the given purpose, look at the butt.
Let the car collapse straight along the highway. We may have a schedule of fallow projections moving at an hour for a given movement (Fig. 13), we will analyze this schedule.
Rice. 13. Graph of the fallow time of the projection
The graph shows that the speed of the car is not regular. It is permissible, it is necessary to know the speed of the car in 30 seconds after the cob of caution (at the point A). Vikoristovuyuchi vyznachennya mitteva ї shvidkostі, we know the module of average ї ї їvidkostі for the interval of an hour from before. For which we can look at a fragment of the graph (Fig. 14).
Rice. 14. Graph of the fallow time of the projection
In order to revise the correctness of the value of the average density, we know the modulus of the average density for the interval between one hour and , let's look at a fragment of the graph (Fig. 15).
Rice. 15. Graph of the fallow time of the projection
We cover the average speed at the given business hour:
They took away two values of the vehicle's speed in 30 seconds after an ear of caution. More precisely, it will be significant, de іnval an hour less, tobto. If you change the time interval more strongly, then you should check the speed of the car at the point A be more accurate.
Mitteva shvidkist - tse vector quantity. To that, krіm її znakhodzhennya (znakhodzhennya її module), it is necessary to know how it is straightened out.
(with) - mitteva shvidkіst
Directly mitt'voi shvidkost zbіgaєtsya іz prіklіshchennya tіla.
If the body collapses curvilinearly, then the mitt is straightened along the dot to the trajectory at this point (Fig. 16).
Head 1
Chi can mitteva shvidkist () change less for direct, without changing for the module?
Solution
On the top, we can look at the stepping butt. The body collapses along a curvilinear trajectory (Fig. 17). Significantly on the trajectory of the move a point A i point B. Significantly directly mitteva ї svidkostі at tsikh points (mitt єva єvydkіst spramirovan according to dotichny to the point of the trajectory). Keep the speed the same for the module and add 5 m/s.
Suggestion: maybe.
Manager 2
Chi can mitteva shvidk_st change only after the module, without changing directly?
Solution
Rice. 18. Illustration before the date
On the little 10 you can see what the points have A i in dots B mitteva shvidkіst straightened however. If the body collapses evenly, then.
Suggestion: maybe.
In this lesson, we started to wrench an uneven rumble, which is the ruckus of swedishness, which is changing. The characteristics of the uneven movement are the average and the mitteva of the sharpness. Understanding about the middle speed is rooted in the apparent replacement of the uneven movement of equals. Some people understand the average speed (like we swayed) more easily, but it’s not suitable for the completion of the head mechanics. That is why it is necessary to understand the mitteva's shvidkost.
List of references
- G.Ya. Myakishev, B.B. Bukhovtsev, N.M. Sotsky. Physics 10. - M: Education, 2008.
- A.P. Rimkevich. physics. Problem book 10-11. - M: Bustard, 2006.
- O.Ya. Savchenko. Head of physics. - M: Nauka, 1988.
- A.V. Perishkin, V.V. Krauklis. Physics course T. 1. - M: Hold. uch.-ped. view. hv. osviti RRFSR, 1957.
- Internet portal "School-collection.edu.ru" ().
- Internet portal "Virtulab.net" ().
Homework
- Nutrition (1-3, 5) as in paragraph 9 (page 24); G.Ya. Myakishev, B.B. Bukhovtsev, N.M. Sotsky. Physics 10 (div. list of recommended literature)
- How is it possible, knowing the average speed for the song interval of an hour, to know the movement, zdijsne body for a part of that interval?
- How does the mitteva shvidkist in case of even rectilinear Russia in the mitteva shvidkost in case of uneven Russia?
- Under the hour їzdi by car, the speedometer readings were taken through the skin quill. How can you calculate the average speed of a car for this money?
- The first third of the cycle, the cyclist traveled 12 km per year, the other third - 16 km per year, and the rest of the third - 24 km per year. Find out the average speed of a bicycle by stretching the mustache path. Give an estimate for km/year
Rolling up the body behind a frail area (Fig. 2);
Rice. 2. Rolling the body along the thin plane ()
Vilne fall (Fig. 3).
See all the ruhu є equal, so that some change their swedishness. At this point, we can see a nervous rumble.
Rivnomirny Rukh mechanical movement, for such a body, for whether or not it is equal to the hour to pass the same day (Fig. 4).
Rice. 4. Equal movement
Rukh is called uneven, if it’s dead for equal intervals, it’s an hour to pass nerіvnі ways.
Rice. 5. Nervnomirny Rukh
The main task of mechanics is to determine the position of the body at any given moment. In the case of uneven Russia, the firmness of the body changes, and it is also necessary to learn how to describe the change in the firmness of the body. For whom, two concepts are introduced: middle swidkіst and mittєva shvidkіst.
The fact of changing the firmness of the body in uneven Russia does not need to be healed, when looking at the movement of the body at a great distance in the whole (we don’t care about the firmness of the skin at the time of the hour), it is necessary to manually introduce the understanding of the average firmness.
For example, a delegation of schoolchildren gets from Novosibirsk Sochi by train. It is about 3300 km to become between these places and the bay. The speed of the train, if only the winds from Novosibirsk became, what does it mean that in the middle of the road the speed was such and on the way to Sochi [M1]? Chi is possible, looming over qі danі, stverdzhuvati, what time we become ruhu (Fig. 6). Of course, the remnants of Novosibirsk city dwellers know that it is about 84 years to get to Sochi.
Rice. 6. Illustration for example
If you look at the movement of the body at the great diversity of the number as a whole, it is better to understand the average density.
Medium swedishness name a new relocation, as if the body was broken, for an hour, for a short relocation (Fig. 7).
Rice. 7. Average swidth
Don't worry about Dane's appointment. For example, an athlete runs 400 m - one colo. The movement of an athlete is good 0 (Fig. 8), but it is clear that even the average speed of zero cannot be good.
Rice. 8. Moved 0
In fact, most victorious is the understanding of the average number of swedishness.
Average road speed- tse vіdnoshnja povnogo shlyakhu, passed by the body, up to an hour, by stretching out this way is passed (Fig. 9).
Rice. 9. Middle shlyakhova shvidkіst
There is one more indication of the average speed.
Medium swedishness- this is the speed, with which the body can collapse evenly, to pass the given time for that very hour, for which it won, it passed, collapsing unevenly.
From the course of mathematics, we know what is the arithmetic mean. For numbers 10 and 36 it is more expensive:
In order to recognize the possibility of victorious formulas for the significance of the average speed, it seems to be the coming task.
manager
The cyclist rides a speed of 10 km/year on a scale, stained glass at a cost of 0.5 years. Dali zі shvidkіstyu 36 km/year descends for 10 hvilin. Find the average speed of a cyclist (Fig. 10).
Rice. 10. Illustration before the date
Given:; ; ;
Know:
Solution:
Oskіlki odinіru danih shvidkost - km / year, those and the average shvidkost know km / year. Otzhe, tsі zavdannya will not be translated into SI. Let's turn it into a yearbook.
Medium speed is good:
The last path () is folded from the path to the pidyom on the shill () and the descent from the schilu ():
The way to go to the skyl dorivnyu:
The way down the slope of the road:
An hour, for which the last path is passed, dorivnyuє:
Suggestion:.
Of course, it is impossible to calculate the arithmetic mean formula for calculating the average speed.
Do not start to understand the average speed of the correlation on the top of the head mechanics. Turning before the order about the train, it is impossible to confirm that the average speed along the entire route of the train is good, then after 5 years we will change the wine to the country from Novosibirsk.
The average swidkist, vymiryanu for an infinitely small interval of an hour, is called mitteva shvidkistyu body(For example: the speedometer of a car (Fig. 11) shows the speed of the vehicle).
Rice. 11. The speedometer of the car shows the speed of the vehicle
Іsnuє sche dne vyznachennya mitteva ї shvidkostі.
Mitteva shvidkist- the movement of the body at the moment of the hour, the movement of the body at this point of the trajectory (Fig. 12).
Rice. 12. Mitteva Shvidkist
To better understand the given purpose, look at the butt.
Let the car collapse straight along the highway. We may have a schedule of fallow projections moving at an hour for a given movement (Fig. 13), we will analyze this schedule.
Rice. 13. Graph of the fallow time of the projection
The graph shows that the speed of the car is not regular. It is permissible, it is necessary to know the speed of the car in 30 seconds after the cob of caution (at the point A). Vikoristovuyuchi vyznachennya mitteva ї shvidkostі, we know the module of average ї ї їvidkostі for the interval of an hour from before. For which we can look at a fragment of the graph (Fig. 14).
Rice. 14. Graph of the fallow time of the projection
In order to revise the correctness of the value of the average density, we know the modulus of the average density for the interval between one hour and , let's look at a fragment of the graph (Fig. 15).
Rice. 15. Graph of the fallow time of the projection
We cover the average speed at the given business hour:
They took away two values of the vehicle's speed in 30 seconds after an ear of caution. More precisely, it will be significant, de іnval an hour less, tobto. If you change the time interval more strongly, then you should check the speed of the car at the point A be more accurate.
Mitteva shvidkist - tse vector quantity. To that, krіm її znakhodzhennya (znakhodzhennya її module), it is necessary to know how it is straightened out.
(with) - mitteva shvidkіst
Directly mitt'voi shvidkost zbіgaєtsya іz prіklіshchennya tіla.
If the body collapses curvilinearly, then the mitt is straightened along the dot to the trajectory at this point (Fig. 16).
Head 1
Chi can mitteva shvidkist () change less for direct, without changing for the module?
Solution
On the top, we can look at the stepping butt. The body collapses along a curvilinear trajectory (Fig. 17). Significantly on the trajectory of the move a point A i point B. Significantly directly mitteva ї svidkostі at tsikh points (mitt єva єvydkіst spramirovan according to dotichny to the point of the trajectory). Keep the speed the same for the module and add 5 m/s.
Suggestion: maybe.
Manager 2
Chi can mitteva shvidk_st change only after the module, without changing directly?
Solution
Rice. 18. Illustration before the date
On the little 10 you can see what the points have A i in dots B mitteva shvidkіst straightened however. If the body collapses evenly, then.
Suggestion: maybe.
In this lesson, we started to wrench an uneven rumble, which is the ruckus of swedishness, which is changing. The characteristics of the uneven movement are the average and the mitteva of the sharpness. Understanding about the middle speed is rooted in the apparent replacement of the uneven movement of equals. Some people understand the average speed (like we swayed) more easily, but it’s not suitable for the completion of the head mechanics. That is why it is necessary to understand the mitteva's shvidkost.
List of references
- G.Ya. Myakishev, B.B. Bukhovtsev, N.M. Sotsky. Physics 10. - M: Education, 2008.
- A.P. Rimkevich. physics. Problem book 10-11. - M: Bustard, 2006.
- O.Ya. Savchenko. Head of physics. - M: Nauka, 1988.
- A.V. Perishkin, V.V. Krauklis. Physics course T. 1. - M: Hold. uch.-ped. view. hv. osviti RRFSR, 1957.
- Internet portal "School-collection.edu.ru" ().
- Internet portal "Virtulab.net" ().
Homework
- Nutrition (1-3, 5) as in paragraph 9 (page 24); G.Ya. Myakishev, B.B. Bukhovtsev, N.M. Sotsky. Physics 10 (div. list of recommended literature)
- How is it possible, knowing the average speed for the song interval of an hour, to know the movement, zdijsne body for a part of that interval?
- How does the mitteva shvidkist in case of even rectilinear Russia in the mitteva shvidkost in case of uneven Russia?
- Under the hour їzdi by car, the speedometer readings were taken through the skin quill. How can you calculate the average speed of a car for this money?
- The first third of the cycle, the cyclist traveled 12 km per year, the other third - 16 km per year, and the rest of the third - 24 km per year. Find out the average speed of a bicycle by stretching the mustache path. Give an estimate for km/year