Difference between movement and path. Path and movement

This term has other meanings, see Movement (meanings).

Moving(in kinematics) - a change in the position of a physical body in space over time relative to the selected reference system.

In relation to the movement of a material point moving called the vector characterizing this change. It has the property of additivity. Usually denoted by the symbol S → (\displaystyle (\vec (S))) - from Italian. s postamento (movement).

The vector modulus S → (\displaystyle (\vec (S))) is the displacement modulus, measured in meters in the International System of Units (SI); in the GHS system - in centimeters.

You can define movement as a change in the radius vector of a point: Δ r → (\displaystyle \Delta (\vec (r))) .

The displacement module coincides with the distance traveled if and only if the direction of velocity does not change during movement. In this case, the trajectory will be a straight line segment. In any other case, for example, with curvilinear motion, it follows from the triangle inequality that the path is strictly longer.

The instantaneous speed of a point is defined as the limit of the ratio of movement to the small period of time during which it was accomplished. More strictly:

V → = lim Δ t → 0 Δ r → Δ t = d r → d t (\displaystyle (\vec (v))=\lim \limits _(\Delta t\to 0)(\frac (\Delta (\vec (r)))(\Delta t))=(\frac (d(\vec (r)))(dt))) .

III. Trajectory, path and movement

The position of a material point is determined in relation to some other, arbitrarily chosen body, called reference body. Contacts him frame of reference– a set of coordinate systems and clocks associated with a reference body.

In the Cartesian coordinate system, the position of point A at a given time relative to this system is characterized by three coordinates x, y and z or a radius vector r– a vector drawn from the origin of the coordinate system to a given point. When a material point moves, its coordinates change over time. r=r(t) or x=x(t), y=y(t), z=z(t) – kinematic equations of a material point.

The main task of mechanics– knowing the state of the system at some initial moment of time t 0 , as well as the laws governing the movement, determine the state of the system at all subsequent moments of time t.

Trajectory movement of a material point - a line described by this point in space. Depending on the shape of the trajectory, there are rectilinear And curvilinear point movement. If the trajectory of a point is a flat curve, i.e. lies entirely in one plane, then the motion of the point is called flat.

The length of the section of the trajectory AB traversed by the material point since the start of time is called path lengthΔs is a scalar function of time: Δs=Δs(t). Unit - meter(m) – the length of the path traveled by light in a vacuum in 1/299792458 s.

IV. Vector method of specifying movement

Radius vector r– a vector drawn from the origin of the coordinate system to a given point. Vector Δ r=r-r 0 , drawn from the initial position of a moving point to its position at a given time is called moving(increment of the radius vector of a point over the considered period of time).

The average velocity vector v> is the ratio of the increment Δr of the radius vector of a point to the time interval Δt: (1). The direction of the average speed coincides with the direction of Δr. With an unlimited decrease in Δt, the average speed tends to a limiting value, which is called the instantaneous speed v. Instantaneous speed is the speed of a body at a given moment of time and at a given point of the trajectory: (2). Instantaneous velocity is a vector quantity equal to the first derivative of the radius vector of a moving point with respect to time.

To characterize the speed of change of speed v points in mechanics, a vector physical quantity called acceleration.

Medium acceleration uneven motion in the interval from t to t+Δt is called a vector quantity equal to the ratio of the change in speed Δ v to the time interval Δt:

Instantaneous acceleration a material point at time t will be the limit of average acceleration: (4). Acceleration A is a vector quantity equal to the first derivative of speed with respect to time.

V. Coordinate method of specifying movement

The position of point M can be characterized by the radius vector r or three coordinates x, y and z: M(x,y,z). The radius vector can be represented as the sum of three vectors directed along the coordinate axes: (5).

From the definition of speed (6). Comparing (5) and (6) we have: (7). Taking into account (7) formula (6) we can write (8). The speed module can be found: (9).

Similarly for the acceleration vector:

(10),

(11),

A natural way to define movement (describing movement using trajectory parameters)

The movement is described by the formula s=s(t). Each point of the trajectory is characterized by its value s. The radius vector is a function of s and the trajectory can be given by the equation r=r(s). Then r=r(t) can be represented as a complex function r. Let's differentiate (14). Value Δs – distance between two points along the trajectory, |Δ r| - the distance between them in a straight line. As the points get closer, the difference decreases. , Where τ – unit vector tangent to the trajectory. , then (13) has the form v=τ v(15). Therefore, the speed is directed tangentially to the trajectory.

Acceleration can be directed at any angle to the tangent to the trajectory of motion. From the definition of acceleration (16). If τ is tangent to the trajectory, then is a vector perpendicular to this tangent, i.e. directed normally. Unit vector, in the normal direction is denoted n. The value of the vector is 1/R, where R is the radius of curvature of the trajectory.

A point located at a distance from the path and R in the direction of the normal n, is called the center of curvature of the trajectory. Then (17). Taking into account the above, formula (16) can be written: (18).

The total acceleration consists of two mutually perpendicular vectors: directed along the trajectory of motion and called tangential, and acceleration directed perpendicular to the trajectory along the normal, i.e. to the center of curvature of the trajectory and called normal.

We find the absolute value of the total acceleration: (19).

Lecture 2 Movement of a material point in a circle. Angular displacement, angular velocity, angular acceleration. Relationship between linear and angular kinematic quantities. Vectors of angular velocity and acceleration.

Lecture outline

Kinematics of rotational motion

In rotational motion, the measure of displacement of the entire body over a short period of time dt is the vector dφ elementary body rotation. Elementary turns (denoted by or) can be considered as pseudovectors (as if).

Angular movement - a vector quantity whose magnitude is equal to the angle of rotation, and the direction coincides with the direction of translational motion right screw (directed along the axis of rotation so that when viewed from its end, the rotation of the body appears to be occurring counterclockwise). The unit of angular displacement is rad.

The rate of change in angular displacement over time is characterized by angular velocity ω . The angular velocity of a rigid body is a vector physical quantity that characterizes the rate of change in the angular displacement of a body over time and is equal to the angular displacement performed by the body per unit time:

Directed vector ω along the axis of rotation in the same direction as dφ (according to the right screw rule). The unit of angular velocity is rad/s

The rate of change in angular velocity over time is characterized by angular acceleration ε

(2).

The vector ε is directed along the axis of rotation in the same direction as dω, i.e. with accelerated rotation, with slow rotation.

The unit of angular acceleration is rad/s2.

During dt an arbitrary point of a rigid body A move to dr, having walked the path ds. From the figure it is clear that dr equal to the vector product of the angular displacement dφ to radius – point vector r : dr =[ dφ · r ] (3).

Linear speed of a point is related to the angular velocity and radius of the trajectory by the relation:

In vector form, the formula for linear speed can be written as vector product: (4)

By definition of the vector product its module is equal to , where is the angle between the vectors and , and the direction coincides with the direction of translational motion of the right propeller as it rotates from to .

Let's differentiate (4) with respect to time:

Considering that - linear acceleration, - angular acceleration, and - linear velocity, we obtain:

The first vector on the right side is directed tangent to the trajectory of the point. It characterizes the change in linear velocity modulus. Therefore, this vector is the tangential acceleration of the point: a τ =[ ε · r ] (7). The tangential acceleration module is equal to a τ = ε · r. The second vector in (6) is directed towards the center of the circle and characterizes the change in the direction of linear velocity. This vector is the normal acceleration of the point: a n =[ ω · v ] (8). Its modulus is equal to a n =ω·v or taking into account that v= ω· r, a n = ω 2 · r= v2 / r (9).

Special cases of rotational motion

With uniform rotation: , hence .

Uniform rotation can be characterized rotation period T- the time it takes for a point to complete one full revolution,

Rotation frequency - the number of full revolutions made by a body during its uniform motion in a circle, per unit of time: (11)

Speed unit - hertz (Hz).

With uniformly accelerated rotational motion :

(13), (14) (15).

Lecture 3 Newton's first law. Force. The principle of independence of acting forces. Resultant force. Weight. Newton's second law. Pulse. Law of conservation of momentum. Newton's third law. Moment of impulse of a material point, moment of force, moment of inertia.

Lecture outline

Newton's first law

Newton's second law

Newton's third law

Moment of impulse of a material point, moment of force, moment of inertia

Newton's first law. Weight. Force

Newton's first law: There are reference systems relative to which bodies move rectilinearly and uniformly or are at rest if no forces act on them or the action of the forces is compensated.

Newton's first law is satisfied only in an inertial frame of reference and asserts the existence of an inertial frame of reference.

Inertia- this is the property of bodies to strive to keep their speed constant.

Inertia call the property of bodies to prevent a change in speed under the influence of an applied force.

Body mass– this is a physical quantity that is a quantitative measure of inertia, it is a scalar additive quantity. Additivity of mass is that the mass of a system of bodies is always equal to the sum of the masses of each body separately. Weight– the basic unit of the SI system.

One form of interaction is mechanical interaction. Mechanical interaction causes deformation of bodies, as well as a change in their speed.

Force– this is a vector quantity that is a measure of the mechanical impact on the body from other bodies, or fields, as a result of which the body acquires acceleration or changes its shape and size (deforms). Force is characterized by its modulus, direction of action, and point of application to the body.

General methods for determining displacements

 1 =X 1  11 +X 2  12 +X 3  13 +…

 2 =X 1  21 +X 2  22 +X 3  23 +…

 3 =X 1  31 +X 2  32 +X 3  33 +…

Work of constant forces: A=P P, P – generalized force– any load (concentrated force, concentrated moment, distributed load),  P – generalized movement(deflection, rotation angle). The designation  mn means movement in the direction of the generalized force “m”, which is caused by the action of the generalized force “n”. Total displacement caused by several force factors:  P = P P + P Q + P M . Movements caused by a single force or a single moment:  – specific displacement . If a unit force P = 1 caused a displacement  P, then the total displacement caused by the force P will be:  P = P P. If the force factors acting on the system are designated X 1, X 2, X 3, etc. , then movement in the direction of each of them:

where X 1  11 =+ 11; X 2  12 =+ 12 ; Х i  m i =+ m i . Dimension of specific movements:

, J-joules, the dimension of work is 1J = 1Nm.

Work of external forces acting on an elastic system:

.

– the actual work under the static action of a generalized force on an elastic system is equal to half the product of the final value of the force and the final value of the corresponding displacement. The work of internal forces (elastic forces) in the case of plane bending:

,

k is a coefficient that takes into account the uneven distribution of tangential stresses over the cross-sectional area and depends on the shape of the section.

Based on the law of conservation of energy: potential energy U=A.

Work reciprocity theorem (Betley's theorem) . Two states of an elastic system:

 1

1 – movement in direction. force P 1 from the action of force P 1;

 12 – movement in direction. force P 1 from the action of force P 2;

 21 – movement in direction. force P 2 from the action of force P 1;

 22 – movement in direction. force P 2 from the action of force P 2.

A 12 =P 1  12 – work done by the force P 1 of the first state on the movement in its direction caused by the force P 2 of the second state. Similarly: A 21 =P 2  21 – work of the force P 2 of the second state on movement in its direction caused by the force P 1 of the first state. A 12 = A 21. The same result is obtained for any number of forces and moments. Work reciprocity theorem: P 1  12 = P 2  21 .

The work of the forces of the first state on displacements in their directions caused by the forces of the second state is equal to the work of the forces of the second state on displacements in their directions caused by the forces of the first state.

Theorem on the reciprocity of displacements (Maxwell's theorem) If P 1 =1 and P 2 =1, then P 1  12 =P 2  21, i.e.  12 = 21, in the general case  mn = nm.

For two unit states of an elastic system, the displacement in the direction of the first unit force caused by the second unit force is equal to the displacement in the direction of the second unit force caused by the first force.

Universal method for determining displacements (linear and rotation angles) – Mohr's method. A unit generalized force is applied to the system at the point for which the generalized displacement is sought. If the deflection is determined, then the unit force is a dimensionless concentrated force; if the angle of rotation is determined, then it is a dimensionless unit moment. In the case of a spatial system, there are six components of internal forces. The generalized displacement is determined by the formula (Mohr's formula or integral):

The line above M, Q and N indicates that these internal forces are caused by a unit force. To calculate the integrals included in the formula, you need to multiply the diagrams of the corresponding forces. The procedure for determining the movement: 1) for a given (real or cargo) system, find the expressions M n, N n and Q n; 2) in the direction of the desired movement, a corresponding unit force (force or moment) is applied; 3) determine efforts

from the action of a single force; 4) the found expressions are substituted into the Mohr integral and integrated over the given sections. If the resulting mn >0, then the displacement coincides with the selected direction of the unit force, if

For flat design:

Usually, when determining displacements, the influence of longitudinal deformations and shear, which are caused by longitudinal N and transverse Q forces, is neglected; only displacements caused by bending are taken into account. For a flat system it will be:

.

IN

calculation of the Mohr integralVereshchagin's method . Integral

for the case when the diagram from a given load has an arbitrary outline, and from a single load it is rectilinear, it is convenient to determine it using the graph-analytical method proposed by Vereshchagin.

, where is the area of the diagram M r from the external load, y c is the ordinate of the diagram from a unit load under the center of gravity of the diagram M r. The result of multiplying diagrams is equal to the product of the area of one of the diagrams and the ordinate of another diagram, taken under the center of gravity of the area of the first diagram. The ordinate must be taken from a straight-line diagram. If both diagrams are straight, then the ordinate can be taken from any one.

P

moving:

. The calculation using this formula is carried out in sections, in each of which the straight-line diagram should be without fractures. A complex diagram M p is divided into simple geometric figures, for which it is easier to determine the coordinates of the centers of gravity. When multiplying two diagrams that have the form of trapezoids, it is convenient to use the formula:

. The same formula is also suitable for triangular diagrams, if you substitute the corresponding ordinate = 0.

P

Under the action of a uniformly distributed load on a simply supported beam, the diagram is constructed in the form of a convex quadratic parabola, the area of which

(for fig.

, i.e.

, x C =L/2).

D

For a “blind” seal with a uniformly distributed load, we have a concave quadratic parabola, for which

;

,

, x C = 3L/4. The same can be obtained if the diagram is represented by the difference between the area of a triangle and the area of a convex quadratic parabola:

. The "missing" area is considered negative.

Castigliano's theorem .

– the displacement of the point of application of the generalized force in the direction of its action is equal to the partial derivative of the potential energy with respect to this force. Neglecting the influence of axial and transverse forces on the movement, we have the potential energy:

, where

.

What is the definition of movement in physics?

Sad Roger

In physics, displacement is the absolute value of a vector drawn from the starting point of a body’s trajectory to the final point. In this case, the shape of the path along which the movement took place (that is, the trajectory itself), as well as the size of this path, does not matter at all. Let's say, the movement of Magellan's ships - well, at least the one that eventually returned (one of three) - is equal to zero, although the distance traveled is wow.

Is Tryfon

Displacement can be viewed in two ways. 1. Change in body position in space. Moreover, regardless of the coordinates. 2. The process of movement, i.e. change in position over time. You can argue about point 1, but to do this you need to recognize the existence of absolute (initial) coordinates.

Movement is a change in the location of a certain physical body in space relative to the reference system used.

This definition is given in kinematics - a subsection of mechanics that studies the movement of bodies and the mathematical description of movement.

Displacement is the absolute value of a vector (that is, a straight line) connecting two points on a path (from point A to point B). Displacement differs from path in that it is a vector value. This means that if the object came to the same point from which it started, then the displacement is zero. But there is no way. A path is the distance an object has traveled due to its movement. To better understand, look at the picture:

What is path and movement from a physics point of view? and what is the difference between them....

very necessary) please answer)

User deleted

Alexander kalapats

Path is a scalar physical quantity that determines the length of the trajectory section traveled by the body during a given time. The path is a non-negative and non-decreasing function of time.
Displacement is a directed segment (vector) connecting the position of the body at the initial moment of time with its position at the final moment of time.
Let me explain. If you leave home, go to visit a friend, and return home, then your path will be equal to the distance between your house and your friend’s house multiplied by two (there and back), and your movement will be equal to zero, because at the final moment of time you will find yourself in the same place as at the initial moment, i.e. at home. A path is a distance, a length, i.e. a scalar quantity that has no direction. Displacement is a directed, vector quantity, and the direction is specified by a sign, i.e., displacement can be negative (If we assume that when you reach your friend’s house you have made a movement s, then when you walk from your friend to his house, you will make a movement -s , where the minus sign means that you walked in the opposite direction to the one in which you walked from the house to your friend).

Forserr33v

Trajectory- this is the line that the body describes when moving.

Bee trajectory

Path is the length of the trajectory. That is, the length of that possibly curved line along which the body moved. Path is a scalar quantity ! Moving- vector quantity ! This is a vector drawn from the initial point of departure of the body to the final point. Has a numerical value equal to the length of the vector. Path and displacement are significantly different physical quantities.

You may come across different path and movement designations:

Amount of movements

Let the body make a movement s 1 during the period of time t 1, and move s 2 during the next period of time t 2. Then for the entire time of movement the displacement s 3 is the vector sum

Uniform movement

Movement with constant speed in magnitude and direction. What does it mean? Consider the motion of a car. If she drives in a straight line, the speedometer shows the same speed value (velocity module), then this movement is uniform. As soon as the car changes direction (turn), it will mean that the velocity vector has changed its direction. The speed vector is directed in the same direction as the car is going. Such movement cannot be considered uniform, despite the fact that the speedometer shows the same number.

The direction of the velocity vector always coincides with the direction of motion of the body

Can the movement on a carousel be considered uniform (if there is no acceleration or braking)? It’s impossible, the direction of movement is constantly changing, and therefore the velocity vector. From the reasoning we can conclude that uniform motion is it is always moving in a straight line! This means that with uniform motion, the path and displacement are the same (explain why).

It is not difficult to imagine that with uniform motion, over any equal periods of time, the body will move the same distance.

A trajectory is a continuous line along which a material point moves in a given reference system. Depending on the shape of the trajectory, rectilinear and curvilinear motion of a material point is distinguished.
Latin Trajectorius - related to movement
Path is the length of a section of the trajectory of a material point traversed by it in a certain time.

The distance traveled is the length of the trajectory section from the start to the end point of movement.

Movement (in kinematics) is a change in the location of a physical body in space relative to the selected reference system. The vector characterizing this change is also called displacement. It has the property of additivity. The length of the segment is the displacement module, measured in meters (SI).

You can define movement as a change in the radius vector of a point: .

The instantaneous speed of a point is defined as the limit of the ratio of movement to the small period of time during which it was accomplished. More strictly:

Average ground speed. Average speed vector. Instant speed.

Average ground speed

Average (ground) speed is the ratio of the length of the path traveled by a body to the time during which this path was covered:

Average ground speed, unlike instantaneous speed, is not a vector quantity.

The average speed is equal to the arithmetic mean of the speeds of the body during movement only in the case when the body moved at these speeds for the same periods of time.

At the same time, if, for example, the car moved half the way at a speed of 180 km/h, and the second half at a speed of 20 km/h, then the average speed will be 36 km/h. In examples like this, the average speed is equal to the harmonic mean of all speeds on individual, equal sections of the path.

Average speed is the ratio of the length of a section of a path to the period of time during which this path is covered.

Average body speed

With uniformly accelerated motion

With uniform movement

Here we used:

Average body speed

Initial speed of the body

Body acceleration

Body movement time

The speed of a body after a certain period of time

Instantaneous speed is the first derivative of the path with respect to time =
v=(ds/dt)=s"
where the symbols d/dt or the dash at the top right of a function indicate the derivative of this function.
Otherwise, this is the speed v = s/t as t tends to zero... :)
In the absence of acceleration at the moment of measurement, the instantaneous value is equal to the average during the period of movement without acceleration Vmg. = Vavg. =S/t for this period.

Let the body move from the initial position at point A to the final position, which is at point C, moving along a trajectory in the shape of an arc ABC. The distance traveled is measured along arc ABC. The length of this arc is the path.

Path is a physical quantity equal to the length

trajectories between the initial position of the body and

its final position. Designated l.

Path units are units of length (m, cm, km,...)

but the basic unit of length is the SI meter. It is written like this

The distance between points A and C is not equal to the length of the path. This is another physical quantity. It's called displacement. Movement has not only a numerical value, but also a certain direction, which depends on the location of the starting and ending points of body movement. Quantities that have not only a modulus (numerical value), but also a direction are called vector quantities or simply vectors.

Moving – this is a vector physical quantity that characterizes the change in the position of a body in space, equal to the length of the segment connecting the point of the initial position of the body with the point of its final position. The movement is directed from the initial position to the final one.

Denoted by . Unit.

Quantities that have no direction, such as path, mass, temperature, are called scalar quantities or scalars.

Can path and movement be equal?

If a body or a material point (MP) moves along a straight line, and always in the same direction, then the path and displacement coincide, i.e. numerically they are equal. So if a stone falls vertically into a gorge 100 m deep, then its movement will be directed downward and s = 100 m. Path l =100 m.

If a body makes several movements, then they are added, but not in the same way as numerical values are added, but according to other rules, according to the rules for adding vectors. You will soon go through them in your math course. For now, let's look at an example.

To get to the bus stop, Pyotr Sergeevich walks first through the courtyard 300 m to the west, and then along the avenue 400 m to the north. Find the displacement of Pyotr Sergeevich and compare it with the distance traveled.

Given: s 1 = 300 m; s 2 = 400 m.

______________________

North

s - ? l - ?

Solution:

West

Let's make a drawing. To find the entire path, add two segments of the path s 1 and s 2

l = s 1 + s 2 = 300 m +400 m = 700 m.

To find the displacement, you need to find out the length of the segment connecting the initial position of the body and the final position. This is the length of the vector s.

Before us is a right triangle with known legs (300 and

400 m). Let's use the Pythagorean theorem to find the length of the hypotenuse s:

Thus, the path traveled by a person is greater than the displacement by 200 m.

If, suppose, Pyotr Sergeevich, having reached the stop, suddenly decided to turn back and moved in the opposite direction, then the length of his path would be 1400 m, and the displacement would be 0 m.

Reference system.

To solve the basic problem of mechanics means to indicate where the body will be at any given moment in time. In other words, calculate the coordinates of the body. But here’s the catch: where will we count the coordinates from?

You can, of course, take geographic coordinates - longitude and latitude, but! Firstly, the body (MT) can move outside the planet Earth. Secondly, the geographic coordinate system does not take into account the three-dimensionality of our space.

First you need to choose reference body. This is so important that otherwise we will find ourselves in a situation similar to that presented in the novel by R. Stevenson “Treasure Island”. Having buried the main part of the treasure, Captain Flint left a map and description of the place.

Tall tree of Spy Mountain. The direction is from the tree along the shade at noon. Walk a hundred feet. Turn towards west. Walk ten fathoms. Dig to a depth of ten inches.

The disadvantage of describing the place where the treasure lies is that the tree, which in this problem is the reference body, cannot be found using the specified characteristics.

This example shows the importance of choice bodies of reference – any body from which the coordinates of the position of a moving material point are measured.

Look at the drawing. As a moving object, take: 1) a yacht; 2) seagull. Take as a body of reference: a) a rock on the shore; b) captain of the yacht; c) a flying seagull. How does the nature of the movement of a moving object and its coordinates depend on the choice of the reference body?

When describing the features of the movement of a particular body, it is important to indicate in relation to which body of reference the characteristics are given.

Let's try to enter the coordinates of the body or MT. Let's use a rectangular Cartesian XYZ coordinate system with the origin at point O. We place the origin of the reference system where the reference body is located. From this point we draw three mutually perpendicular coordinate axes OX, OY, OZ. Now the coordinates of the material point (x;y;z) can be indicated relative to the reference body.

To study body movement (BMT), you also need a watch or a device for measuring time. We will associate the start of the countdown with a specific event. Most often this is the beginning of body movement (MT).

The combination of a reference body, a coordinate system associated with the reference body and a device for measuring time intervals is called reference system (CO) .

If a stationary body is chosen as a reference body, then the reference system will also be stationary (NSO). Most often, the surface of the Earth is chosen as a stationary body of reference. You can choose a moving body as the reference body and get moving frame of reference(PSO).

Look at Figure 1. A three-dimensional coordinate system allows you to specify the position in space of any point. For example, the coordinates of point F located on the column are equal to (6; 3; 1).

-2 - 1 0 1 2 3 4 5 6 7 8 9 10 X

Think! Which coordinate system will you choose when solving problems related to movement:

1) a cyclist participates in competitions on a cycling track;

2) a fly crawls on the glass;

3) a fly flies around the kitchen;

4) the truck is moving along a straight section of the highway;

5) a person goes up in an elevator;

6) the projectile takes off and flies from the muzzle of the gun.

Exercise 1.

1. Select in Fig. 3 the cases in which mechanical movement occurs.

3.There are two operators at the flight control center. One controls the orbital parameters of the Mir station, and the other docks the Progress spacecraft with this station. Which operator can consider the Mir station to be a material point?

4. To study the movement of a fighter plane and a hot air balloon (Fig. 4), the rectangular coordinate system XOYZ was chosen. Describe the frame of reference that is used here. Could simpler coordinate systems be used?

5. The athlete ran a 400-meter distance (Fig. 5). Find the movement of the athlete and the path traveled by him.

6. Figure 6 shows a leaf of a plant on which a snail is crawling. Using a scale grid, calculate the path traveled by the snail from point A to point B and from point B to point C.

7. The car, having driven along a straight section of the highway from a gas station to the nearest populated area, returned back. Calculate the modulus of displacement of the machine and the distance traveled by it. What can be said about the relationship between the displacement module and the distance traveled if the car only traveled from a gas station to a populated area?

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If we take into account the physical processes in the domestic sphere, many of them seem to be very good. Therefore, the concepts of path and movement are perceived as one and the same, the only difference is that the first is a description of the action, and the second is the result of the action. But if you turn to information sources for clarification, you can immediately find a significant difference between these operations.

What is the path?

A path is a movement that results in a change in the location of an object or person. This quantity is a scalar quantity, so it has no direction, but it can be used to determine the distance traveled.

The path can be executed in the following ways:

In a straight line.
Curvilinear.
Round.
Other methods are possible (for example, a zigzag trajectory).

The path can never be negative and decrease over time. The distance is measured in meters. Most often, in physics the letter is used to designate a path S, in rare cases, the letter L is used. Using a path, we cannot predict where the object we need will be at a certain point in time.

Features of movement

Displacement is the difference between the starting and ending points of the location of a person or object in space after some path has been covered.

The displacement value is always positive and also has a clear direction.

A coincidence between movement and path is possible only if the path was carried out in a straight line, and the direction did not change.

Using movement, you can calculate where a person or object was at a certain point in time.

To denote movement, the letter S is used, but since movement is a vector quantity, an arrow → is placed above this letter, which indicates that movement is a vector. Unfortunately, adding to the confusion between path and movement is the fact that both concepts can also be denoted by the letter L.

What do the concepts path and movement have in common?

Despite the fact that path and movement are completely different concepts, there are certain elements that contribute to the concepts being confused:

Path and displacement can always only be positive quantities.
The same letter L can be used to indicate path and movement.

Even considering the fact that these concepts have only two common elements, their meaning is so great that it makes many people confused. Schoolchildren especially have problems when studying physics.

The main differences between the concepts of path and movement?

These concepts have a number of differences that will always help you determine what quantity is in front of you, path or movement:

Path is the primary concept, and movement is secondary. For example, movement determines the difference between the starting and ending points of a person’s location in space after covering a certain path. Accordingly, it is impossible to obtain the displacement value without using the path initially.
The beginning of the movement plays a huge role for the path, but the beginning of the movement is absolutely not necessary to determine the movement.
The main difference between these quantities is that the path has no direction, but movement does. For example, the path is carried out only straight forward, but movement also allows for backward movement.
In addition, the concepts differ in appearance. Path refers to a scalar quantity, and displacement refers to a vector quantity.
Calculus method. For example, a path is calculated using the total distance traveled, and displacement, in turn, is calculated using a change in the location of an object in space.
Path can never be zero, but movement is allowed to be zero.

Having studied these differences, you can immediately understand what the difference is between the concepts of path and movement, and never confuse them again.

Difference between path and movement with examples

In order to quickly understand the difference between path and movement, you can use certain examples:

The car moved 2 meters forward and 2 meters backward. The path is the sum of the total distance traveled, so it is 4 meters. And the displacement is the starting and ending point, so in this case it is equal to zero.
In addition, the difference between path and movement can be seen from your own experience. You need to stand at the start of a 400-meter treadmill and run two laps (the second lap will end at the starting point). The result is that the path was 800 meters (400+400), and the displacement is 0, since the start and end points are the same.
The ball thrown upward reached a height of 15 meters and then fell to the Earth. In this case, the path will be 30 meters, since 15 meters up and 15 meters down are added. And the displacement will be equal to 0, due to the fact that the ball has returned to its original position.