Average moving speed. Average ground speed. Uniform linear motion Uneven speed

1. Uniform movement occurs infrequently. Generally, mechanical motion is motion with varying speed. A movement in which the speed of a body changes over time is called uneven.

For example, traffic moves unevenly. The bus, starting to move, increases its speed; When braking, its speed decreases. Bodies falling on the Earth's surface also move unevenly: their speed increases over time.

With uneven movement, the coordinate of the body can no longer be determined using the formula x = x 0 + v x t, since the speed of movement is not constant. The question arises: what value characterizes the speed of change in body position over time with uneven movement? This quantity is average speed.

Medium speed vWeduneven movement is called physical quantity, equal to the displacement ratio sbodies by time t for which it was committed:

Average speed is vector quantity. To determine the average velocity module for practical purposes, this formula can be used only in the case when the body moves along a straight line in one direction. In all other cases, this formula is unsuitable.

Let's look at an example. It is necessary to calculate the time of arrival of the train at each station along the route. However, the movement is not linear. If you calculate the module of the average speed in the section between two stations using the above formula, the resulting value will differ from the value of the average speed at which the train was moving, since the module of the displacement vector is less than the distance traveled by the train. And the average speed of movement of this train from the starting point to the final point and back, in accordance with the above formula, is completely zero.

In practice, when determining the average speed, a value equal to path relation l In time t, during which this path was passed:

v Wed = .

She is often called average ground speed.

2. Knowing the average speed of a body at any part of the trajectory, it is impossible to determine its position at any time. Let's assume that the car traveled 300 km in 6 hours. The average speed of the car is 50 km/h. However, at the same time, he could stand for some time, move for some time at a speed of 70 km/h, for some time - at a speed of 20 km/h, etc.

Obviously, knowing the average speed of a car in 6 hours, we cannot determine its position after 1 hour, after 2 hours, after 3 hours, etc.

3. When moving, the body passes sequentially all points of the trajectory. At each point it is at certain times and has some speed.

Instantaneous speed is the speed of a body in this moment time or at a given point in the trajectory.

Let us assume that the body makes uneven linear motion. Let us determine the speed of movement of this body at the point O its trajectory (Fig. 21). Let us select a section on the trajectory AB, inside which there is a point O. Moving s 1 in this area the body has completed in time t 1 . The average speed in this section is v avg 1 = .

Let's reduce body movement. Let it be equal s 2, and the movement time is t 2. Then the average speed of the body during this time: v avg 2 = .Let us further reduce the movement, the average speed in this section is: v cf 3 = .

We will continue to reduce the time of movement of the body and, accordingly, its displacement. Eventually, the movement and time will become so small that a device, such as a speedometer in a car, will no longer record the change in speed and the movement over this short period of time can be considered uniform. The average speed in this area is the instantaneous speed of the body at the point O.

Thus,

instantaneous speed is a vector physical quantity equal to the ratio of small displacement D sto a short period of time D t, during which this movement was completed:

Self-test questions

1. What kind of movement is called uneven?

2. What is average speed?

3. What does average ground speed indicate?

4. Is it possible, knowing the trajectory of a body and its average speed over a certain period of time, to determine the position of the body at any moment in time?

5. What is instantaneous speed?

6. How do you understand the expressions “small movement” and “short period of time”?

Task 4

1. The car drove along Moscow streets 20 km in 0.5 hours, when leaving Moscow it stood for 15 minutes, and in the next 1 hour 15 minutes it drove 100 km around the Moscow region. At what average speed did the car move in each section and along the entire route?

2. What is the average speed of a train on a stretch between two stations if it traveled the first half of the distance between stations at an average speed of 50 km/h, and the second half at an average speed of 70 km/h?

3. What is the average speed of a train on a stretch between two stations if it traveled half the time at an average speed of 50 km/h, and the remaining time at an average speed of 70 km/h?

With uneven motion, a body can travel both equal and different paths in equal periods of time.

To describe uneven motion, the concept is introduced average speed.

Average speed, by this definition, is a scalar quantity because the path and time are scalar quantities.

However, the average speed can also be determined through displacement according to the equation

The average speed of a path and the average speed of movement are two different quantities that can characterize the same movement.

When calculating average speed, a mistake is often made in that the concept of average speed is replaced by the concept of the arithmetic mean of the speed of the body in different areas of movement. To show the illegality of such a substitution, consider the problem and analyze its solution.

From point A train leaves for point B. For half the entire journey the train moves at a speed of 30 km/h, and for the second half of the journey at a speed of 50 km/h.

What is the average speed of the train on section AB?

The movement of the train on section AC and section CB is uniform. Looking at the text of the problem, you often immediately want to give the answer: υ av = 40 km/h.

Yes, because it seems to us that the formula used to calculate the arithmetic average is quite suitable for calculating the average speed.

Let's see: is it possible to use this formula and calculate the average speed by finding the half-sum of the given speeds.

To do this, let's consider a slightly different situation.

Let's say we're right and the average speed is really 40 km/h.

Then let's solve another problem.

As you can see, the problem texts are very similar, there is only a “very small” difference.

If in the first case we are talking about half the journey, then in the second case we are talking about half the time.

Obviously, point C in the second case is somewhat closer to point A than in the first case, and it is probably impossible to expect the same answers in the first and second problems.

If, when solving the second problem, we also give the answer that the average speed is equal to half the sum of the speeds in the first and second sections, we cannot be sure that we solved the problem correctly. What should I do?

The way out of the situation is as follows: the fact is that average speed is not determined through the arithmetic mean. There is a defining equation for average speed, according to which, to find the average speed in a certain area, the entire path traveled by the body must be divided by the entire time of movement:

We need to start solving the problem with the formula that determines the average speed, even if it seems to us that in some case we can use a simpler formula.

We will move from the question to known quantities.

We express the unknown quantity υ avg through other quantities – L 0 and Δ t 0 .

It turns out that both of these quantities are unknown, so we must express them in terms of other quantities. For example, in the first case: L 0 = 2 ∙ L, and Δ t 0 = Δ t 1 + Δ t 2.

Let us substitute these values, respectively, into the numerator and denominator of the original equation.

In the second case we do exactly the same. We don't know the whole path and all the time. We express them: and

It is obvious that the travel time on section AB in the second case and the travel time on section AB in the first case are different.

In the first case, since we do not know the times and we will try to express these quantities: and in the second case we express and:

We substitute the expressed quantities into the original equations.

Thus, in the first problem we have:

After transformation we get:

In the second case we get and after the transformation:

The answers, as predicted, are different, but in the second case we found that the average speed is indeed equal to half the sum of the speeds.

The question may arise: why can’t we immediately use this equation and give such an answer?

The point is that, having written down that the average speed in section AB in the second case is equal to half the sum of the speeds in the first and second sections, we would imagine not a solution to a problem, but a ready-made answer. The solution, as you can see, is quite long, and it begins with the defining equation. The fact that in this case we received the equation that we wanted to use initially is pure coincidence.

With uneven movement, the speed of a body can continuously change. With such movement, the speed at any subsequent point of the trajectory will differ from the speed at the previous point.

The speed of a body at a given moment of time and at a given point of the trajectory is called instantaneous speed.

The longer the time period Δt, the more the average speed differs from the instantaneous one. And, conversely, the shorter the time period, the less the average speed differs from the instantaneous speed of interest to us.

Let us define the instantaneous speed as the limit to which the average speed tends over an infinitesimal period of time:

If we are talking about the average speed of movement, then the instantaneous speed is a vector quantity:

If we are talking about the average speed of a path, then the instantaneous speed is a scalar quantity:

There are often cases when, during uneven motion, the speed of a body changes over equal periods of time by the same amount.

With uniform motion, the speed of a body can either decrease or increase.

If the speed of a body increases, then the movement is called uniformly accelerated, and if it decreases, it is called uniformly slow.

A characteristic of uniformly alternating motion is a physical quantity called acceleration.

Knowing the acceleration of the body and its initial speed, you can find the speed at any predetermined moment in time:

In projection onto the coordinate axis 0X, the equation will take the form: υ ​​x = υ 0 x + a x ∙ Δ t.

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

Note 1

Uneven motion is characterized by the fact that a body can travel the same or different paths in equal periods of time.

To fully understand this type of mechanical motion, the 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:

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

By this definition, average speed is a scalar quantity, since time and distance 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 travel characterize the same movement, but they are different quantities.

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

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

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

$L_0$ and $\Delta t_0$.

We get a formula according to which the search for an unknown quantity is carried out:

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

When solving a long chain of equations, one can arrive at 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 continuously changes. 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.

Instantaneous speed

Instantaneous speed is the speed in a given period of time at a certain point on the trajectory.

The average speed of a body will differ more from the instantaneous speed in cases where:

• it is greater than the time interval $\Delta t$;
• it is less than a period of time.

Definition 2

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

Instantaneous speed becomes a vector quantity when talking about the average speed of movement.

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

With uneven motion, a change in the speed of a body occurs over equal periods of time by an equal amount.

Uniform motion of a body occurs at the moment when the speed of an object changes by an equal amount over any equal periods of time.

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

The speed can vary by numerical value. Such movement is also considered uneven. Uniformly accelerated motion is considered a special case of uneven motion.

Definition 3

Unequally variable motion is the movement of a body when the speed of the object does not change by a certain amount over any unequal periods of time.

Equally variable motion is characterized by the possibility of increasing or decreasing the speed of a body.

Motion is called uniformly slow when the speed of a body decreases. Uniformly accelerated motion is a motion in which the speed of a body increases.

Acceleration

For uneven motion, one more characteristic has been introduced. This physical quantity is called acceleration.

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

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

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

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

In order to obtain a 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 a body and its initial speed, you can find the speed at any given moment in advance.

A physical quantity that is equal to the ratio of the path traveled by a body in a specific period of time to the duration of such an interval is the average ground speed. Average ground speed is expressed as:

• scalar quantity;
• non-negative value.

The average speed is represented in vector form. It is directed to where the movement of the body is directed over a certain period of time.

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

Uniform movement- this is movement at a constant speed, that is, when the speed does not change (v = const) and acceleration or deceleration does not occur (a = 0).

Straight-line movement- this is movement in a straight line, that is, the trajectory of rectilinear movement is a straight line.

This is a movement in which a body makes equal movements at any equal intervals of time. For example, if we divide a certain time interval into one-second intervals, then with uniform motion the body will move the same distance for each of these time intervals.

The speed of uniform rectilinear motion does not depend on time and at each point of the trajectory is directed in the same way as the movement of the body. That is, the displacement vector coincides in direction with the velocity vector. In this case, the average speed for any period of time is equal to the instantaneous speed:

Speed ​​of uniform rectilinear motion is a physical vector quantity equal to the ratio of the movement of a body over any period of time to the value of this interval t:

=/t

Thus, the speed of uniform rectilinear motion shows how much movement a material point makes per unit time.

Moving with uniform linear motion is determined by the formula:

Distance traveled in linear motion is equal to the displacement module. If the positive direction of the OX axis coincides with the direction of movement, then the projection of the velocity onto the OX axis is equal to the magnitude of the velocity and is positive:

The projection of displacement onto the OX axis is equal to:

where x 0 is the initial coordinate of the body, x is the final coordinate of the body (or the coordinate of the body at any time)

Equation of motion, that is, the dependence of the body coordinates on time x = x(t), takes the form:

If the positive direction of the OX axis is opposite to the direction of motion of the body, then the projection of the body’s velocity onto the OX axis is negative, the speed is less than zero (v< 0), и тогда уравнение движения принимает вид:

Uniform linear movement- This is a special case of uneven motion.

Uneven movement- this is a movement in which a body (material point) makes unequal movements over equal periods of time. For example, a city bus moves unevenly, since its movement consists mainly of acceleration and deceleration.

Equally alternating motion- this is a movement in which the speed of a body (material point) changes equally over any equal periods of time.

Acceleration of a body during uniform motion remains constant in magnitude and direction (a = const).

Uniform motion can be uniformly accelerated or uniformly decelerated.

Uniformly accelerated motion- this is the movement of a body (material point) with positive acceleration, that is, with such movement the body accelerates with constant acceleration. In the case of uniformly accelerated motion, the modulus of the body’s velocity increases over time, and the direction of acceleration coincides with the direction of the speed of movement.

Equal slow motion- this is the movement of a body (material point) with negative acceleration, that is, with such movement the body uniformly slows down. In uniformly slow motion, the velocity and acceleration vectors are opposite, and the velocity modulus decreases over time.

In mechanics, any rectilinear motion is accelerated, therefore slow motion differs from accelerated motion only in the sign of the projection of the acceleration vector onto the selected axis of the coordinate system.

Average variable speed is determined by dividing the movement of the body by the time during which this movement was made. The unit of average speed is m/s.

This is the speed of a body (material point) at a given moment of time or at a given point of the trajectory, that is, the limit to which the average speed tends with an infinite decrease in the time interval Δt:

Instantaneous velocity vector uniformly alternating motion can be found as the first derivative of the displacement vector with respect to time:

= "

Velocity vector projection on the OX axis:

this is the derivative of the coordinate with respect to time (the projections of the velocity vector onto other coordinate axes are similarly obtained).

This is a quantity that determines the rate of change in the speed of a body, that is, the limit to which the change in speed tends with an infinite decrease in the time interval Δt:

Acceleration vector of uniformly alternating motion can be found as the first derivative of the velocity vector with respect to time or as the second derivative of the displacement vector with respect to time:

= " = " Considering that 0 is the speed of the body at the initial moment of time (initial speed), is the speed of the body at a given moment of time (final speed), t is the period of time during which the change in speed occurred, will be as follows:

From here uniform speed formula at any time:

0 + t If a body moves rectilinearly along the OX axis of a rectilinear Cartesian coordinate system, coinciding in direction with the body’s trajectory, then the projection of the velocity vector onto this axis is determined by the formula:

The “-” (minus) sign in front of the projection of the acceleration vector refers to uniformly slow motion. The equations for projections of the velocity vector onto other coordinate axes are written similarly.

Since in uniform motion the acceleration is constant (a = const), the acceleration graph is a straight line parallel to the 0t axis (time axis, Fig. 1.15).

Rice. 1.15. Dependence of body acceleration on time.

Dependence of speed on time is a linear function, the graph of which is a straight line (Fig. 1.16).

Rice. 1.16. Dependence of body speed on time.

Speed ​​versus time graph(Fig. 1.16) shows that

In this case, the displacement is numerically equal to the area of ​​the figure 0abc (Fig. 1.16).

The area of ​​a trapezoid is equal to the product of half the sum of the lengths of its bases and its height. The bases of the trapezoid 0abc are numerically equal:

The height of the trapezoid is t. Thus, the area of ​​the trapezoid, and therefore the projection of displacement onto the OX axis is equal to:

In the case of uniformly slow motion, the acceleration projection is negative and in the formula for the displacement projection a “-” (minus) sign is placed before the acceleration.

A graph of the velocity of a body versus time at various accelerations is shown in Fig. 1.17. The graph of displacement versus time for v0 = 0 is shown in Fig. 1.18.

Rice. 1.17. Dependence of body speed on time for different acceleration values.

Rice. 1.18. Dependence of body movement on time.

The speed of the body at a given time t 1 is equal to the tangent of the angle of inclination between the tangent to the graph and the time axis v = tg α, and the displacement is determined by the formula:

If the time of movement of the body is unknown, you can use another displacement formula by solving a system of two equations:

It will help us derive the formula for displacement projection:

Since the coordinate of the body at any moment in time is determined by the sum of the initial coordinate and the displacement projection, it will look like this:

The graph of the coordinate x(t) is also a parabola (like the graph of displacement), but the vertex of the parabola in the general case does not coincide with the origin. When a x< 0 и х 0 = 0 ветви параболы направлены вниз (рис. 1.18).

Rolling the body down an inclined plane (Fig. 2);

Rice. 2. Rolling the body down an inclined plane ()

Free fall (Fig. 3).

All these three types of movement are not uniform, that is, their speed changes. In this lesson we will look at uneven motion.

Uniform movement - mechanical movement in which a body travels the same distance in any equal periods of time (Fig. 4).

Rice. 4. Uniform movement

Movement is called uneven, in which the body travels unequal paths in equal periods of time.

Rice. 5. Uneven movement

The main task of mechanics is to determine the position of the body at any moment in time. When the body moves unevenly, the speed of the body changes, therefore, it is necessary to learn to describe the change in the speed of the body. To do this, two concepts are introduced: average speed and instantaneous speed.

The fact of a change in the speed of a body during uneven movement does not always need to be taken into account; when considering the movement of a body over a large section of the path as a whole (the speed at each moment of time is not important to us), it is convenient to introduce the concept of average speed.

For example, a delegation of schoolchildren travels from Novosibirsk to Sochi by train. The distance between these cities is railway is approximately 3300 km. The speed of the train when it just left Novosibirsk was , does this mean that in the middle of the journey the speed was like this same, but at the entrance to Sochi [M1]? Is it possible, having only these data, to say that the travel time will be (Fig. 6). Of course not, since residents of Novosibirsk know that it takes approximately 84 hours to get to Sochi.

Rice. 6. Illustration for example

When considering the movement of a body over a large section of the path as a whole, it is more convenient to introduce the concept of average speed.

Medium speed they call the ratio of the total movement that the body has made to the time during which this movement was made (Fig. 7).

Rice. 7. Average speed

This definition is not always convenient. For example, an athlete runs 400 m - exactly one lap. The athlete’s displacement is 0 (Fig. 8), but we understand that his average speed cannot be zero.

Rice. 8. Displacement is 0

In practice, the concept of average ground speed is most often used.

Average ground speed is the ratio of the total path traveled by the body to the time during which the path was traveled (Fig. 9).

Rice. 9. Average ground speed

There is another definition of average speed.

average speed- this is the speed with which a body must move uniformly in order to cover a given distance in the same time in which it passed it, moving unevenly.

From the mathematics course we know what the arithmetic mean is. For numbers 10 and 36 it will be equal to:

In order to find out the possibility of using this formula to find the average speed, let's solve the following problem.

Task

A cyclist climbs a slope at a speed of 10 km/h, spending 0.5 hours. Then it goes down at a speed of 36 km/h in 10 minutes. Find the average speed of the cyclist (Fig. 10).

Rice. 10. Illustration for the problem

Given:; ; ;

Find:

Solution:

Since the unit of measurement for these speeds is km/h, we will find the average speed in km/h. Therefore, we will not convert these problems into SI. Let's convert to hours.

The average speed is:

The full path () consists of the path up the slope () and down the slope ():

The path to climb the slope is:

The path down the slope is:

The time it takes to travel the full path is:

Answer:.

Based on the answer to the problem, we see that it is impossible to use the arithmetic mean formula to calculate the average speed.

The concept of average speed is not always useful for solving the main problem of mechanics. Returning to the problem about the train, it cannot be said that if the average speed along the entire journey of the train is equal to , then after 5 hours it will be at a distance from Novosibirsk.

The average speed measured over an infinitesimal period of time is called instantaneous speed of the body(for example: a car’s speedometer (Fig. 11) shows instantaneous speed).

Rice. 11. Car speedometer shows instantaneous speed

There is another definition of instantaneous speed.

Instantaneous speed– the speed of movement of the body at a given moment in time, the speed of the body at a given point of the trajectory (Fig. 12).

Rice. 12. Instant speed

In order to better understand this definition, let's look at an example.

Let the car move straight along a section of highway. We have a graph of the projection of displacement versus time for a given movement (Fig. 13), let’s analyze this graph.

Rice. 13. Graph of displacement projection versus time

The graph shows that the speed of the car is not constant. Let's say you need to find the instantaneous speed of a car 30 seconds after the start of observation (at the point A). Using the definition of instantaneous speed, we find the magnitude of the average speed over the time interval from to . To do this, consider a fragment of this graph (Fig. 14).

Rice. 14. Graph of displacement projection versus time

In order to check the correctness of finding the instantaneous speed, let’s find the average speed module for the time interval from to , for this we consider a fragment of the graph (Fig. 15).

Rice. 15. Graph of displacement projection versus time

We calculate the average speed over a given period of time:

We obtained two values ​​of the instantaneous speed of the car 30 seconds after the start of observation. More accurate will be the value where the time interval is smaller, that is. If we decrease the time interval under consideration more strongly, then the instantaneous speed of the car at the point A will be determined more accurately.

Instantaneous speed is a vector quantity. Therefore, in addition to finding it (finding its module), it is necessary to know how it is directed.

(at ) – instantaneous speed

The direction of instantaneous velocity coincides with the direction of movement of the body.

If a body moves curvilinearly, then the instantaneous speed is directed tangentially to the trajectory at a given point (Fig. 16).

Exercise 1

Can instantaneous speed () change only in direction, without changing in magnitude?

Solution

To solve this, consider the following example. The body moves along a curved path (Fig. 17). Let's mark a point on the trajectory of movement A and period B. Let us note the direction of the instantaneous velocity at these points (the instantaneous velocity is directed tangentially to the trajectory point). Let the velocities and be equal in magnitude and equal to 5 m/s.

Answer: Maybe.

Task 2

Can instantaneous speed change only in magnitude, without changing in direction?

Solution

Rice. 18. Illustration for the problem

Figure 10 shows that at the point A and at the point B instantaneous speed is in the same direction. If a body moves uniformly accelerated, then .

Answer: Maybe.

In this lesson, we began to study uneven movement, that is, movement with varying speed. The characteristics of uneven motion are average and instantaneous speeds. The concept of average speed is based on the mental replacement of uneven motion with uniform motion. Sometimes the concept of average speed (as we have seen) is very convenient, but it is not suitable for solving the main problem of mechanics. Therefore, the concept of instantaneous speed is introduced.

Bibliography

1. G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10. - M.: Education, 2008.
2. A.P. Rymkevich. Physics. Problem book 10-11. - M.: Bustard, 2006.
3. O.Ya. Savchenko. Physics problems. - M.: Nauka, 1988.
4. A.V. Peryshkin, V.V. Krauklis. Physics course. T. 1. - M.: State. teacher ed. min. education of the RSFSR, 1957.

1. Internet portal “School-collection.edu.ru” ().
2. Internet portal “Virtulab.net” ().

Homework

1. Questions (1-3, 5) at the end of paragraph 9 (page 24); G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10 (see list of recommended readings)
2. Is it possible, knowing the average speed over a certain period of time, to find the displacement made by a body during any part of this interval?
3. What is the difference between instantaneous speed during uniform linear motion and instantaneous speed during uneven motion?
4. While driving a car, speedometer readings were taken every minute. Is it possible to determine the average speed of a car from these data?
5. The cyclist rode the first third of the route at a speed of 12 km per hour, the second third at a speed of 16 km per hour, and the last third at a speed of 24 km per hour. Find the average speed of the bike over the entire journey. Give your answer in km/hour