A message about rectilinear and curvilinear motion. Curvilinear movement

With the help of this lesson you can independently study the topic “Rectilinear and curvilinear motion. Movement of a body in a circle with a constant absolute speed." First, we will characterize rectilinear and curvilinear motion by considering how in these types of motion the velocity vector and the force applied to the body are related. Next we will consider special case when a body moves in a circle with a constant absolute speed.

In the previous lesson we looked at issues related to the law universal gravity. The topic of today's lesson is closely related to this law; we will turn to the uniform motion of a body in a circle.

We said earlier that movement - This is a change in the position of a body in space relative to other bodies over time. Movement and direction of movement are also characterized by speed. The change in speed and the type of movement itself are associated with the action of force. If a force acts on a body, then the body changes its speed.

If the force is directed parallel to the movement of the body, then such movement will be straightforward(Fig. 1).

Rice. 1. Straight-line movement

Curvilinear there will be such a movement when the speed of the body and the force applied to this body are directed relative to each other at a certain angle (Fig. 2). In this case, the speed will change its direction.

Rice. 2. Curvilinear movement

So, when straight motion the velocity vector is directed in the same direction as the force applied to the body. A curvilinear movement is such a movement when the velocity vector and the force applied to the body are located at a certain angle to each other.

Let us consider a special case of curvilinear motion, when a body moves in a circle with a constant velocity in absolute value. When a body moves in a circle with constant speed, then only the direction of speed changes. In absolute value it remains constant, but the direction of the velocity changes. This change in speed leads to the presence of acceleration in the body, which is called centripetal.

Rice. 6. Movement along a curved path

If the trajectory of a body’s movement is a curve, then it can be represented as a set of movements along circular arcs, as shown in Fig. 6.

In Fig. Figure 7 shows how the direction of the velocity vector changes. The speed during such a movement is directed tangentially to the circle along the arc of which the body moves. Thus, its direction is constantly changing. Even if the absolute speed remains constant, a change in speed leads to acceleration:

In this case acceleration will be directed towards the center of the circle. That's why it's called centripetal.

Why is centripetal acceleration directed towards the center?

Recall that if a body moves along a curved path, then its speed is directed tangentially. Velocity is a vector quantity. A vector has a numerical value and a direction. The speed continuously changes its direction as the body moves. That is, the difference in speeds at different times will not be equal to zero (), unlike a straight line uniform motion.

So, we have a change in speed over a certain period of time. The ratio to is acceleration. We come to the conclusion that, even if the speed does not change in absolute value, a body performing uniform motion in a circle has acceleration.

Where is this acceleration directed? Let's look at Fig. 3. Some body moves curvilinearly (along an arc). The speed of the body at points 1 and 2 is directed tangentially. The body moves uniformly, that is, the velocity modules are equal: , but the directions of the velocities do not coincide.

Rice. 3. Body movement in a circle

Subtract the speed from it and get the vector. To do this, you need to connect the beginnings of both vectors. In parallel, move the vector to the beginning of the vector. We build up to a triangle. The third side of the triangle will be the velocity difference vector (Fig. 4).

Rice. 4. Velocity difference vector

The vector is directed towards the circle.

Let's consider a triangle formed by the velocity vectors and the difference vector (Fig. 5).

Rice. 5. Triangle formed by velocity vectors

This triangle is isosceles (the velocity modules are equal). This means that the angles at the base are equal. Let us write down the equality for the sum of the angles of a triangle:

Let's find out where the acceleration is directed at a given point on the trajectory. To do this, we will begin to bring point 2 closer to point 1. With such unlimited diligence, the angle will tend to 0, and the angle will tend to . The angle between the velocity change vector and the velocity vector itself is . The speed is directed tangentially, and the vector of speed change is directed towards the center of the circle. This means that the acceleration is also directed towards the center of the circle. That is why this acceleration is called centripetal.

How to find centripetal acceleration?

Let's consider the trajectory along which the body moves. In this case it is a circular arc (Fig. 8).

Rice. 8. Body movement in a circle

The figure shows two triangles: a triangle formed by velocities, and a triangle formed by radii and displacement vector. If points 1 and 2 are very close, then the displacement vector will coincide with the path vector. Both triangles are isosceles with the same vertex angles. Thus, the triangles are similar. This means that the corresponding sides of the triangles are equally related:

The displacement is equal to the product of speed and time: . Substituting this formula, we can obtain the following expression for centripetal acceleration:

Angular velocity denoted by the Greek letter omega (ω), it indicates the angle through which the body rotates per unit time (Fig. 9). This is the magnitude of the arc in degrees passed by the body over some time.

Rice. 9. Angular velocity

Please note that if solid rotates, then the angular velocity for any points on this body will be a constant value. Closer point whether it is located towards the center of rotation or further - this does not matter, i.e. it does not depend on the radius.

The unit of measurement in this case will be either degrees per second () or radians per second (). Often the word “radian” is not written, but simply written. For example, let’s find what the angular velocity of the Earth is. The Earth makes a complete rotation in one hour, and in this case we can say that the angular velocity is equal to:

Also pay attention to the relationship between angular and linear speeds:

Linear speed is directly proportional to the radius. The larger the radius, the greater the linear speed. Thus, moving away from the center of rotation, we increase our linear speed.

It should be noted that circular motion at a constant speed is a special case of motion. However, the movement around the circle may be uneven. The speed can change not only in direction and remain the same in magnitude, but also change in its value, i.e., in addition to a change in direction, there is also a change in the velocity magnitude. In this case we are talking about the so-called accelerated motion in a circle.

What is a radian?

There are two units for measuring angles: degrees and radians. In physics, as a rule, the radian measure of angle is the main one.

Let's construct a central angle that rests on an arc of length .

Movement is a change of position
bodies in space relative to others
bodies over time. Movement and
direction of movement is characterized in
including speed. Change
speed and the type of movement itself are related to
by the action of force. If the body is affected
force, then the body changes its speed.

Centripetal acceleration

Angular velocity. relationship between angular and linear speeds

Finished works

DEGREE WORKS

Much has already passed and now you are a graduate, if, of course, you write your thesis on time. But life is such a thing that only now it becomes clear to you that, having ceased to be a student, you will lose all the student joys, many of which you have never tried, putting everything off and putting it off until later. And now, instead of catching up, you're working on your thesis? There is an excellent solution: download the thesis you need from our website - and you will instantly have a lot of free time!
Theses have been successfully defended at leading universities of the Republic of Kazakhstan.
Cost of work from 20,000 tenge

COURSE WORKS

The course project is the first serious practical work. It is with the writing of the coursework that preparation for development begins. diploma projects. If a student learns to correctly present the content of a topic in a course project and format it competently, then in the future he will not have problems either writing reports or compiling theses, nor with the implementation of others practical tasks. To assist students in writing this type of student work and to clarify questions that arise during its preparation, in fact, this information section was created.
Cost of work from 2,500 tenge

MASTER'S DISSERTATIONS

Currently in higher educational institutions In Kazakhstan and the CIS countries, the level of higher education is very common vocational education, which follows a bachelor's degree - a master's degree. In the master's program, students study with the aim of obtaining a master's degree, which is recognized in most countries of the world more than a bachelor's degree, and is also recognized by foreign employers. The result of master's studies is the defense of a master's thesis.
We will provide you with up-to-date analytical and textual material, the price includes 2 science articles and abstract.
Cost of work from 35,000 tenge

PRACTICE REPORTS

After completing any type of student internship (educational, industrial, pre-graduation), a report is required. This document will be confirmation practical work student and the basis for forming an assessment for practice. Usually, in order to draw up a report on an internship, you need to collect and analyze information about the enterprise, consider the structure and work routine of the organization in which the internship is taking place, draw up a calendar plan and describe your practical activities.
We will help you write a report on your internship, taking into account the specifics of the activities of a particular enterprise.

Mechanical movement. Relativity of mechanical motion. Reference system

Mechanical motion is understood as a change over time in the relative position of bodies or their parts in space: for example, the movement of celestial bodies, vibrations earth's crust, air and sea currents, movement aircraft and vehicles, machines and mechanisms, deformation of structural elements and structures, movement of liquids and gases, etc.

Relativity of mechanical motion

We have been familiar with the relativity of mechanical motion since childhood. So, sitting on a train and watching a train, which was previously standing on a parallel track, start moving, we often cannot determine which of the trains actually started moving. And here we should immediately clarify: move relative to what? Regarding the Earth, of course. Because we began to move relative to the neighboring train, regardless of which of the trains began its movement relative to the Earth.

The relativity of mechanical motion lies in the relativity of the speeds of movement of bodies: the speeds of bodies relative to different reference systems will be different (the speed of a person moving in a train, ship, airplane will differ both in magnitude and in direction, depending on the reference system in which these speeds are determined: in the reference system associated with the moving vehicle, or with a stationary Earth).

The trajectories of body movement in different systems countdown. For example, drops of rain falling vertically onto the ground will leave a mark in the form of oblique streams on the window of a moving train. In the same way, any point on the rotating propeller of a flying airplane or a helicopter descending to the ground describes a circle relative to the airplane and a much more complex curve - a helical line relative to the Earth. Thus, when mechanical movement the trajectory of movement is also relative.

The path traveled by the body also depends on the frame of reference. Returning to the same passenger sitting on the train, we understand that the path he made relative to the train during the trip equal to zero(if he did not move around the carriage) or, in any case, much less than the distance that he covered with the train relative to the Earth. Thus, with mechanical motion, the path is also relative.

The awareness of the relativity of mechanical motion (i.e., that the movement of a body can be considered in different reference systems) led to the transition from the geocentric system of the world of Ptolemy to the heliocentric system of Copernicus. Ptolemy, following the movement of the Sun and stars in the sky observed since ancient times, placed the stationary Earth in the center of the Universe with the rest rotating around it celestial bodies. Copernicus believed that the Earth and other planets rotate around the Sun and at the same time around their axes.

Thus, a change in the reference system (Earth - in geocentric system world and the Sun - in heliocentric) led to a much more progressive heliocentric system, which makes it possible to solve many scientific and applied problems of astronomy and change humanity’s views on the Universe.

The coordinate system $X, Y, Z$, the reference body with which it is associated, and the device for measuring time (clock) form a reference system relative to which the movement of the body is considered.

Reference body called the body relative to which the change in the position of other bodies in space is considered.

The reference system can be chosen arbitrarily. In kinematic studies, all reference systems are equal. In dynamics problems, you can also use any arbitrarily moving reference frames, but inertial reference frames are most convenient, since in them the characteristics of motion have a simpler form.

Material point

A material point is an object of negligible size that has mass.

The concept of “material point” is introduced to describe (using mathematical formulas) mechanical movement of bodies. This is done because it is easier to describe the movement of a point than a real body, whose particles can also move with at different speeds(for example, during body rotation or deformation).

If a real body is replaced by a material point, then the mass of this body is assigned to this point, but its dimensions are neglected, and at the same time the difference in the characteristics of the movement of its points (velocities, accelerations, etc.), if any, is neglected. In what cases can this be done?

Almost any body can be considered as a material point if the distances passable points bodies are very large compared to its size.

For example, the Earth and other planets are considered material points when studying their movement around the Sun. In this case, differences in the movement of various points of any planet, caused by its daily rotation, do not affect the quantities describing the annual movement.

Consequently, if in the motion of a body under study one can neglect its rotation around an axis, such a body can be represented as a material point.

However, when solving problems related to the daily rotation of planets (for example, when determining the sunrise at different places surfaces globe), it makes no sense to consider a planet a material point, since the result of the problem depends on the size of this planet and the speed of movement of points on its surface.

It is legitimate to consider an airplane as a material point if it is necessary, for example, to determine the average speed of its movement on the way from Moscow to Novosibirsk. But when calculating the air resistance force acting on a flying airplane, it cannot be considered a material point, since the resistance force depends on the size and shape of the airplane.

If a body moves translationally, even if its dimensions are comparable to the distances it travels, this body can be considered as a material point (since all points of the body move the same way).

In conclusion, we can say: a body whose dimensions can be neglected in the conditions of the problem under consideration can be considered a material point.

Trajectory

A trajectory is a line (or, as they say, a curve) that a body describes when moving relative to a selected body of reference.

It makes sense to talk about a trajectory only in the case when the body can be represented as a material point.

Trajectories may have different shapes. It is sometimes possible to judge the shape of a trajectory by the visible trace left by a moving body, for example, a flying airplane or a meteor streaking through the night sky.

The shape of the trajectory depends on the choice of reference body. For example, relative to the Earth, the trajectory of the Moon is a circle; relative to the Sun, it is a line of a more complex shape.

When studying mechanical motion, the Earth is usually considered as a body of reference.

Methods for specifying the position of a point and describing its movement

The position of a point in space is specified in two ways: 1) using coordinates; 2) using the radius vector.

The position of a point using coordinates is specified by three projections of the point $x, y, z$ on the axis Cartesian system coordinates $OX, OU, OZ$ associated with the reference body. To do this, from point A it is necessary to lower perpendiculars on the plane $YZ$ (coordinate $x$), $ХZ$ (coordinate $y$), $ХУ$ (coordinate $z$), respectively. It is written like this: $A(x, y, z)$. For a specific case, $(x=6, y=10.2, z= 4.5$), point $A$ is designated $A(6; 10; 4.5)$.

On the contrary, if specific values ​​of the coordinates of a point in a given coordinate system are given, then to depict the point itself it is necessary to plot the coordinate values ​​on the corresponding axes ($x$ to the $OX$ axis, etc.) and construct a parallelepiped on these three mutually perpendicular segments. Its vertex, opposite the origin of coordinates $O$ and lying on the diagonal of the parallelepiped, will be the desired point $A$.

If a point moves within a certain plane, then it is enough to draw two coordinate axes through the points selected on the reference body: $OX$ and $OU$. Then the position of the point on the plane is determined by two coordinates $x$ and $y$.

If a point moves along a straight line, it is enough to set one coordinate axis OX and direct it along the line of movement.

Setting the position of point $A$ using the radius vector is carried out by connecting point $A$ to the origin of coordinates $O$. The directed segment $OA = r↖(→)$ is called the radius vector.

Radius vector is a vector connecting the origin with the position of a point at an arbitrary moment in time.

A point is specified by a radius vector if its length (modulus) and direction in space are known, i.e., the values ​​of its projections $r_x, r_y, r_z$ on the coordinate axes $OX, OY, OZ$, or the angles between the radius vector and coordinate axes. For the case of motion on a plane we have:

Here $r=|r↖(→)|$ is the module of the radius vector $r↖(→), r_x$ and $r_y$ are its projections on the coordinate axes, all three quantities are scalars; xzhu - coordinates of point A.

The last equations demonstrate the connection between the coordinate and vector methods of specifying the position of a point.

The vector $r↖(→)$ can also be decomposed into components along the $X$ and $Y$ axes, i.e., represented as the sum of two vectors:

$r↖(→)=r↖(→)_x+r↖(→)_y$

Thus, the position of a point in space is specified either by its coordinates or by the radius vector.

Ways to describe the movement of a point

In accordance with the methods of specifying coordinates, the movement of a point can be described: 1) by coordinate method; 2) vector method.

With the coordinate method of describing (or specifying) movement, the change in the coordinates of a point over time is written in the form of functions of all three of its coordinates versus time:

The equations are called kinematic equations of motion of a point, written in coordinate form. Knowing the kinematic equations of motion and initial conditions (i.e., the position of the point at the initial time), you can determine the position of the point at any time.

With the vector method of describing the movement of a point, the change in its position over time is given by the dependence of the radius vector on time:

$r↖(→)=r↖(→)(t)$

The equation is the equation of motion of a point, written in vector form. If it is known, then for any moment in time it is possible to calculate the radius vector of the point, i.e. determine its position (as in the case of the coordinate method). Thus, specifying three scalar equations is equivalent to specifying one vector equation.

For each case of motion, the form of the equations will be quite specific. If the trajectory of a point’s movement is a straight line, the movement is called rectilinear, and if it is a curve, it is called curvilinear.

Movement and path

Displacement in mechanics is a vector connecting the positions of a moving point at the beginning and at the end of a certain period of time.

The concept of a displacement vector is introduced to solve the problem of kinematics - to determine the position of a body (point) in space at a given moment in time, if its initial position is known.

In Fig. the vector $(M_1M_2)↖(-)$ connects two positions of a moving point - $M_1$ and $M_2$ at times $t_1$ and $t_2$ respectively and, according to definition, is a displacement vector. If point $M_1$ is specified by the radius vector $r↖(→)_1$, and point $M_2$ is specified by the radius vector $r↖(→)_2$, then, as can be seen from the figure, the displacement vector is equal to the difference of these two vectors , i.e., the change in the radius vector over time $∆t=t_2-t_1$:

$∆r↖(→)=r↖(→)_2-r↖(→)_1$.

Addition of movements (for example, on two neighboring areas trajectories) $∆r↖(→)_1$ and $∆r↖(→)_2$ is carried out according to the vector addition rule:

$∆r=∆r↖(→)_2+∆r↖(→)_1$

The path is the length of the trajectory section traveled by a material point during a given period of time. The magnitude of the displacement vector in the general case is not equal to the length of the path traveled by the point during the time $∆t$ (the trajectory can be curvilinear, and, in addition, the point can change the direction of movement).

The magnitude of the displacement vector is equal to the path only for rectilinear motion in one direction. If the direction of linear motion changes, the magnitude of the displacement vector is less than the path.

During curvilinear motion, the magnitude of the displacement vector is also less than the path, since the chord is always less than the length of the arc that it subtends.

Velocity of a material point

Speed ​​characterizes the speed with which any changes occur in the world around us (the movement of matter in space and time). The movement of a pedestrian along the sidewalk, the flight of a bird, the propagation of sound, radio waves or light in the air, the flow of water from a pipe, the movement of clouds, the evaporation of water, the heating of an iron - all these phenomena are characterized by a certain speed.

In the mechanical movement of bodies, speed characterizes not only the speed, but also the direction of movement, i.e. vector quantity.

The speed $υ↖(→)$ of a point is the limit of the ratio of the movement $∆r↖(→)$ to the time interval $∆t$ during which this movement occurred, as $∆t$ tends to zero (i.e., the derivative $∆r↖(→)$ by $t$):

$υ↖(→)=(lim)↙(∆t→0)(∆r↖(→))/(∆t)=r↖(→)_1"$

The components of the velocity vector along the $X, Y, Z$ axes are determined similarly:

$υ↖(→)_x=(lim)↙(∆t→0)(∆x)/(∆t)=x"; υ_y=y"; υ_z=z"$

The concept of speed defined in this way is also called instantaneous speed. This definition of speed is valid for any type of movement - from curvilinear uneven to rectilinear uniform. When they talk about speed during uneven motion, it means instantaneous speed. The vector nature of speed directly follows from this definition, since moving- vector quantity. The instantaneous velocity vector $υ↖(→)$ is always directed tangentially to the motion trajectory. It indicates the direction in which the body would move if, from the moment of time $t$, the action of any other bodies on it ceased.

average speed

The average speed of a point is introduced to characterize uneven motion (i.e., motion with variable speed) and is determined in two ways.

1. The average speed of a point $υ_(av)$ is equal to the ratio of the entire path $∆s$ traversed by the body to the entire time of movement $∆t$:

$υ↖(→)_(avg)=(∆s)/(∆t)$

With this definition, the average speed is a scalar, since the distance traveled (distance) and time are scalar quantities.

This method of determination gives an idea of average speed of movement on the trajectory section (average ground speed).

2. The average speed of a point is equal to the ratio of the point’s movement to the period of time during which this movement occurred:

$υ↖(→)_(avg)=(∆r↖(→))/(∆t)$

The average speed of movement is a vector quantity.

For uneven curvilinear motion, such a definition of the average speed does not always make it possible to determine even approximately the real speeds along the path of the point’s movement. For example, if a point moved along a closed path for some time, then its displacement is equal to zero (but the speed was clearly different from zero). In this case, it is better to use the first definition of average speed.

In any case, you should distinguish between these two definitions of average speed and know which one you are talking about.

Law of addition of speeds

The law of addition of velocities establishes a connection between the values ​​of the velocity of a material point relative to various systems reference points moving relative to each other. In non-relativistic (classical) physics, when the speeds under consideration are small compared to the speed of light, Galileo’s law of addition of speeds is valid, which is expressed by the formula:

$υ↖(→)_2=υ↖(→)_1+υ↖(→)$

where $υ↖(→)_2$ and $υ↖(→)_1$ are the velocities of the body (point) relative to two inertial systems reference - a stationary reference system $K_2$ and a reference system $K_1$ moving with a speed $υ↖(→)$ relative to $K_2$.

The formula can be obtained by adding the displacement vectors.

For clarity, let us consider the movement of a boat with a speed of $υ↖(→)_1$ relative to the river (reference frame $K_1$), the waters of which move with a speed of $υ↖(→)$ relative to the shore (reference frame $K_2$).

The displacement vectors of the boat relative to the water $∆r↖(→)_1$, the river relative to the shore $∆r↖(→)$ and the total displacement vector of the boat relative to the shore $∆r↖(→)_2$ are shown in Fig..

Mathematically:

$∆r↖(→)_2=∆r↖(→)_1+∆r↖(→)$

Dividing both sides of the equation by the time interval $∆t$, we get:

$(∆r↖(→)_2)/(∆t)=(∆r↖(→)_1)/(∆t)+(∆r↖(→))/(∆t)$

In the projections of the velocity vector on the coordinate axes, the equation has the form:

$υ_(2x)=υ_(1x)+υ_x,$

$υ_(2y)=υ_(1y)+υ_y.$

The velocity projections are added algebraically.

Relative speed

From the law of addition of velocities it follows that if two bodies move in the same reference frame with velocities $υ↖(→)_1$ and $υ↖(→)_2$, then the speed of the first body relative to the second $υ↖(→) _(12)$ is equal to the difference in the velocities of these bodies:

$υ↖(→)_(12)=υ↖(→)_1-υ↖(→)_2$

Thus, when bodies move in one direction (overtaking), the relative velocity module is equal to the difference in speeds, and when moving in the opposite direction, it is the sum of the speeds.

Acceleration of a material point

Acceleration is a quantity characterizing the rate of change of speed. As a rule, the movement is uneven, that is, it occurs at a variable speed. In some parts of a body's trajectory, the speed may be greater, in others - less. For example, a train leaving a station moves faster and faster over time. Approaching the station, he, on the contrary, slows down.

Acceleration (or instantaneous acceleration) - vector physical quantity, equal to the limit of the ratio of the change in speed to the time period during which this change occurred, as $∆t$ tends to zero, (i.e., the derivative of $υ↖(→)$ with respect to $t$):

$a↖(→)=lim↙(∆t→0)(∆υ↖(→))/(∆t)=υ↖(→)_t"$

The components $a↖(→) (a_x, a_y, a_z)$ ​​are equal, respectively:

$a_x=υ_x";a_y=υ_y";a_z=υ_z"$

Acceleration, like the change in speed, is directed towards the concavity of the trajectory and can be decomposed into two components - tangential- tangentially to the trajectory of movement - and normal- perpendicular to the trajectory.

In accordance with this, the projection of acceleration $а_х$ onto the tangent to the trajectory is called tangent, or tangential acceleration, projection $a_n$ onto the normal - normal, or centripetal acceleration.

Tangential acceleration determines the amount of change in the numerical value of speed:

$a_t=lim↙(∆t→0)(∆υ)/(∆t)$

Normal, or centripetal acceleration characterizes the change in the direction of speed and is determined by the formula:

where R is the radius of curvature of the trajectory at its corresponding point.

The acceleration module is determined by the formula:

$a=√(a_t^2+a_n^2)$

In rectilinear motion, the total acceleration $a$ is equal to the tangential one $a=a_t$, since the centripetal one $a_n=0$.

The SI unit of acceleration is the acceleration at which the speed of a body changes by 1 m/s for every second. This unit is denoted 1 m/s 2 and is called “meter per second squared”.

Uniform linear movement

The motion of a point is called uniform if it travels equal distances in any equal periods of time.

For example, if a car travels 20 km for every quarter hour (15 minutes), 40 km for every half hour (30 minutes), 80 km for every hour (60 minutes), etc., then such movement is considered uniform. With uniform motion, the numerical value (modulus) of the speed of the point $υ$ is a constant value:

$υ=|υ↖(→)|=const$

Uniform movement can occur both along a curved and along a rectilinear trajectory.

The law of uniform motion of a point is described by the equation:

where $s$ is the distance measured along the trajectory arc from a certain point on the trajectory taken as the origin; $t$ - time of a point on the way; $s_0$ - value of $s$ at the initial moment of time $t=0$.

The path traveled by a point in time $t$ is determined by the term $υt$.

Uniform linear movement- this is a movement in which a body moves with a constant speed in magnitude and direction:

$υ↖(→)=const$

The speed of uniform rectilinear motion is a constant value and can be defined as the ratio of the movement of a point to the period of time during which this movement occurred:

$υ↖(→)=(∆r↖(→))/(∆t)$

Module of this speed

$υ=(|∆r↖(→)|)/(∆t)$

in meaning, it is the distance $s=|∆r↖(→)|$ traveled by the point during the time $∆t$.

The speed of a body in uniform rectilinear motion is a quantity equal to the ratio of the path $s$ to the time during which this path is covered:

Displacement during linear uniform motion (along the X axis) can be calculated using the formula:

where $υ_x$ is the projection of velocity onto the X axis. Hence the law of rectilinear uniform motion has the form:

If at the initial moment of time $x_0=0$, then

The graph of speed versus time is a straight line parallel to the x-axis, and the distance traveled is the area under this straight line.

The graph of the path versus time is a straight line, the angle of inclination of which to the time axis $Ot$ is greater, the greater the speed of uniform motion. The tangent of this angle is equal to the speed.