Movement with varying speed is considered to be uneven. The speed can vary in direction. It can be concluded that any movement NOT along a straight path is uneven. For example, the movement of a body in a circle, the movement of a body thrown into the distance, etc.

The speed can be changed numerically. This movement will also be uneven. A special case of such a movement is uniformly accelerated movement.

Sometimes there is uneven traffic, which consists of alternating different types of movements, for example, first the bus accelerates (the movement is uniformly accelerated), then it moves evenly for some time, and then stops.

Instant speed

Uneven movement can only be characterized by speed. But the speed is always changing! Therefore, we can only talk about speed at a given moment in time. When traveling by car, the speedometer shows you the instantaneous speed of movement every second. But in this case, the time must be reduced not to a second, but to consider a much shorter period of time!

average speed

What is average speed? It is wrong to think that it is necessary to add up all instantaneous speeds and divide by their number. This is the most common misconception about average speed! Average speed is divide the whole path by the elapsed time... And it is not determined in any other way. If we consider the movement of the car, we can estimate its average speeds in the first half of the journey, in the second, along the entire journey. Average speeds can be the same, or they can be different in these areas.

A horizontal line is drawn on top of the averages.

Average travel speed. Average ground speed

If the movement of the body is not rectilinear, then the path traversed by the body will be greater than its movement. In this case, the average travel speed differs from the average ground speed. Ground speed is a scalar.

The main thing to remember

1) Definition and types of uneven movement;
2) The difference between the average and instantaneous speeds;
3) The rule of finding the average speed of movement

It is often required to solve a problem where the entire path is divided into equal sections, given the average speed for each section, it is required to find the average speed of movement along the entire path. The wrong decision will be if you add up the average speeds and divide by their number. Below is a formula that can be used to solve similar problems.

Instantaneous speed can be determined using the driving graph. The instantaneous speed of a body at any point on the graph is determined by the slope of the tangent to the curve at the corresponding point. Instantaneous speed is the tangent of the slope of the tangent to the graph of the function.

Exercises

While driving the car, the speedometer readings were taken every minute. Is it possible to determine the average speed of the vehicle from this data?

It is impossible, since in the general case the value of the average speed is not equal to the arithmetic mean of the values ​​of instantaneous speeds. And the way and time are not given.

What is the speed of the variable movement shown by the car speedometer?

Close to instant. Close, since the time interval should be infinitely small, and when taking readings from the speedometer, you cannot judge the time like that.

When are instantaneous and average speeds equal? Why?

With uniform movement. Because the speed does not change.

The speed of the hammer on impact is 8m / s. What speed is it: average or instant?

In real life, it is very difficult to meet uniform motion, since objects of the material world cannot move with such great accuracy, and even for a long period of time, therefore, in practice, a more real physical concept is usually used that characterizes the movement of a certain body in space and time.

Remark 1

Uneven movement is characterized by the fact that the body can travel the same or different paths at equal intervals of time.

For a complete understanding of this type of mechanical motion, an additional concept of average speed is introduced.

average speed

Definition 1

Average speed is a physical quantity that is equal to the ratio of the entire path traveled by the body to the total time of movement.

This indicator is considered in a specific area:

$ \ upsilon = \ frac (\ Delta S) (\ Delta t) $

According to this definition, the average speed is a scalar quantity, since time and path are scalar quantities.

The average speed can be determined by the displacement equation:

The average speed in such cases is considered a vector quantity, since it can be determined through the ratio of the vector quantity to the scalar quantity.

The average speed of movement and the average speed of passing the path characterize the same movement, however, they are different values.

In the process of calculating the average speed, error is usually made. It consists in the fact that the concept of average speed is sometimes replaced by the arithmetic average speed of a body. This defect is allowed in different areas of body movement.

The average body speed cannot be determined through the arithmetic mean. To solve the problems, the equation for the average speed is used. It can be used to find the average speed of the body in a certain area. To do this, divide the entire path that the body has traveled by the total time of movement.

The unknown value $ \ upsilon $ can be expressed in terms of others. They are designated:

$ L_0 $ and $ \ Delta t_0 $.

It turns out the formula according to which the unknown quantity is being searched:

$ L_0 = 2 ∙ L $, and $ \ Delta t_0 = \ Delta t_1 + \ Delta t_2 $.

When solving a long chain of equations, you can come to the original version of searching for the average speed of a body in a certain area.

With continuous movement, the speed of the body also changes continuously. Such a movement gives rise to a pattern in which the speed at any subsequent points of the trajectory differs from the speed of the object at the previous point.

Instant speed

Instantaneous speed is the speed at a given time interval at a certain point on the trajectory.

The average body speed will differ more from the instantaneous speed in cases when:

• it is more than the time interval $ \ Delta t $;
• it is less than the time span.

Definition 2

Instantaneous speed is a physical quantity that is equal to the ratio of a small movement on a certain part of the trajectory or the distance traveled by the body to a short period of time during which this movement was made.

Instantaneous speed becomes a vector when it comes to the average speed of movement.

Instantaneous speed becomes a scalar when talking about the average speed of a path.

With an uneven movement, the change in the speed of the body occurs at equal intervals of time by an equal amount.

Equally variable motion of the body occurs at the moment when the speed of the object for any equal time intervals changes by an equal amount.

Types of uneven movement

With uneven movement, the speed of the body constantly changes. There are main types of uneven movement:

• movement in a circle;
• movement of a body thrown into the distance;
• uniformly accelerated motion;
• equal slow motion;
• equal motion
• uneven motion.

The speed can be changed numerically. This movement is also considered uneven. A special case of uneven movement is considered to be uniformly accelerated movement.

Definition 3

Unequal motion is such a motion of a body when the speed of an object for any unequal time intervals does not change by a certain amount.

Equivalent movement is characterized by the ability to increase or decrease the speed of the body.

Equally slow motion is when the speed of the body decreases. Equally accelerated is the movement in which the speed of the body increases.

Acceleration

One more characteristic has been introduced for uneven movement. This physical quantity is called acceleration.

Acceleration is called a vector physical quantity equal to the ratio of the change in the speed of the body to the time when this change occurred.

$ a = \ frac (\ upsilon) (t) $

With uniform motion, there is no dependence of the acceleration on the change in the speed of the body, as well as on the time of the change in this speed.

Acceleration indicates a quantitative change in the speed of a body for a certain unit of time.

In order to obtain the unit of acceleration, it is necessary to substitute the units of speed and time into the classical formula for acceleration.

In projection onto the 0X coordinate axis, the equation will take the following form:

$ υx = υ0x + ax ∙ \ Delta t $.

If you know the acceleration of the body and its initial speed, you can find the speed in advance at any given moment in time.

The physical quantity, which is equal to the ratio of the path traversed by the body for a specific period of time, to the duration of such an interval, is the average ground speed. Average ground speed is expressed as:

• scalar;
• non-negative value.

Average speed is shown as a vector. It is directed to where the body moves over a certain period of time.

The modulus of the average speed is equal to the average ground speed in cases where the body is moving in one direction all this time. The modulus of the average speed decreases to the average ground speed if, in the process of movement, the body changes the direction of its movement.

Equally accelerated curvilinear motion

Curvilinear movements are movements whose trajectories are not straight lines, but curved lines. Planets and river waters move along curvilinear trajectories.

Curvilinear movement is always movement with acceleration, even if the modulus of the velocity is constant. Curvilinear motion with constant acceleration always occurs in the plane in which the acceleration vectors and initial velocities of the point are located. In the case of curvilinear motion with constant acceleration in the xOy plane, the projections vx and vy of its velocities on the Ox and Oy axes and the x and y coordinates of the point at any time t is determined by the formulas

Irregular movement. Irregular motion speed

No body moves at a constant speed all the time. Starting movement, the car moves faster and faster. It can move evenly for a while, but then it slows down and stops. In this case, the car travels different distances in the same time.

A movement in which the body passes unequal segments of the path at equal intervals of time is called uneven. With such a movement, the magnitude of the speed does not remain unchanged. In this case, we can only talk about average speed.

The average speed shows what the displacement that the body passes per unit of time is equal to. It is equal to the ratio of the movement of the body to the time of movement. Average speed, like the speed of a body in uniform motion, is measured in meters divided by a second. In order to characterize movement more accurately, instantaneous speed is used in physics.

The speed of a body at a given moment in time or at a given point on the trajectory is called instantaneous speed. Instantaneous velocity is a vector quantity and is directed in the same way as a displacement vector. You can measure your instantaneous speed using a speedometer. In the International System, instantaneous speed is measured in meters divided by a second.

point movement speed uneven

Body movement in a circle

Curvilinear movement is very common in nature and technology. It is more difficult than rectilinear, since there are many curvilinear trajectories; this movement is always accelerated, even when the speed module does not change.

But movement along any curved path can be roughly represented as movement along the arcs of a circle.

When the body moves in a circle, the direction of the velocity vector changes from point to point. Therefore, when they talk about the speed of such a movement, they mean instantaneous speed. The velocity vector is directed tangentially to the circle, and the displacement vector is directed along the chords.

Uniform movement along a circle is a movement during which the modulus of the movement speed does not change, only its direction changes. The acceleration of such a movement is always directed towards the center of the circle and is called centripetal. In order to find the acceleration of a body that moves in a circle, it is necessary to divide the square of the speed by the radius of the circle.

In addition to acceleration, the movement of a body in a circle is characterized by the following quantities:

The period of rotation of the body is the time during which the body makes one complete revolution. The period of rotation is indicated by the letter T and is measured in seconds.

The body's rotational speed is the number of revolutions per unit of time. The rotational speed is indicated by the letter? and is measured in hertz. In order to find the frequency, it is necessary to divide the unit by the period.

Linear velocity is the ratio of body movement to time. In order to find the linear velocity of a body in a circle, it is necessary to divide the circumference by the period (the circumference is equal to 2 times the radius).

Angular velocity is a physical quantity equal to the ratio of the angle of rotation of the radius of the circle along which the body moves to the time of movement. The angular velocity is indicated by the letter? and is measured in radians divided by a second. You can find the angular velocity by dividing 2? for a period of. Angular velocity and linear velocity among themselves. In order to find the linear velocity, the angular velocity must be multiplied by the radius of the circle.

Figure 6. Circular motion, formulas.

Mechanical movement is the change in the position of a body in space over time relative to other bodies.

Based on the definition, the fact of body movement can be established by comparing its position at successive times with the position of another body, which is called the reference body.

So, watching the ball on the football field, we can say that it changes its position relative to the goal or relative to the foot of a football player.The ball, which is rolling on the floor, changes its position relative to the floor. The residential building is at rest relative to the Earth, but changes its position relative to the Sun.

Mechanical movement trajectory

Trajectory Is the line along which the body moves. For example, the trail of an airplane in the sky and the trail of a tear on the cheek are all trajectories of body movement. Motion paths can be straight, curved, or broken. But the length of the trajectory, or the sum of the lengths, is the path traversed by the body.

The path is indicated by the letter S. And is measured in meters, centimeters and kilometers.

There are other units of measure for length.

Types of mechanical movement: uniform and uneven movement