Abstract on the topic of rectilinear uniformly accelerated motion. Lesson summary: "Rectilinear uniformly accelerated motion. Acceleration." slide: III. Learning new material

Graphical representation of uniform rectilinear motion Upr 4 (2) V ; km/h (Time) t, s

Acceleration [a] \u003d m / s 2 a \u003d V / t m / s: c \u003d m / s 2 - the speed of change of speed. (how much the speed of the body changes per second) (a value equal to the ratio of the change in the speed of the body to the time period during which this change occurred) V 0 - initial speed V - final speed V - change in speed t - time

1 question. Choose the correct statement(s): A. Uniformly accelerated motion is non-uniform motion. B. uniformly accelerated motion is uniform. 1) only A; 2) only B; 3) both A and B; 4) neither A nor B. Which of the formulas corresponds to the definition of acceleration? 1) a \u003d υ 2 / 2s; 2) a \u003d (υ-υ 0) / t; 3) a \u003d υ / t; 4) a \u003d (υ 0 -υ) / t

2 question. In what units is acceleration measured? 1)km/h; 2) m / s 2; 3) km / h 2; 4) m2/s; Which statement(s) is/are true? A. If the direction of acceleration coincides with the direction of speed, then the modulus of speed increases. B. If the direction of acceleration is opposite to the direction of speed, then the modulus of speed decreases. 1) Only A; 2) only B; 3) both A and B; 4) neither A nor B.

3 question. Which statement(s) is/are true? A. If the direction of acceleration is opposite to the direction of speed, then the modulus of speed decreases. B. if the direction of acceleration coincides with the direction of speed, then the modulus of speed increases. 1) both A and B; 2) neither A nor B. 3) only A; 4) only B; What physical quantity is a vector? 1) acceleration; 2) displacement projection; 3) time; 4) way.

4 question. The motorcyclist begins to move from a state of rest. After 30 s, it reaches a speed of 15 m/s. What is the acceleration of the movement? 1) 2 m / s 2; 2) 30 m / s 2; 3) 15 m / s 2; 4) 0.5 m/s 2. The sled rolled down the snow hill with uniform acceleration. Their speed at the end of the descent is 12 m/s. Descent time 6 s. With what acceleration did the movement occur if the descent began from a state of rest. 1) 2 m / s 2; 2) 6 m / s 2; 3) 12 m / s 2; 4) 0.5 m/s 2.

5 question. The sled drove down the mountain and drove onto another. During the ascent to the mountain, the speed of the sledge, moving in a straight line and uniformly accelerated, changed from 12 to 2 m/s in 4 s. In this case, the acceleration is: 1) -2.5 m / s 2; 2) 2.5 m / s 2; 3) -3 m / s 2; 4) 3 m/s 2. During rectilinear uniformly accelerated motion for 2 s, the speed of the ball decreased from 8 to 3 m/s. With what acceleration was the ball moving? 1) - 0.4 m / s 2; 2) 4 m / s 2; 3) -2.5 m / s 2; 4) 2.5 m/s 2.

6 question. A cyclist is moving down a hill with uniform acceleration and in a straight line. During the descent, its speed increased by 10 m/s. The acceleration of the cyclist is 0.5 m/s 2. How long did the descent last? The acceleration of a body in a rectilinear uniformly accelerated motion is 2 m / s 2. In what time will its speed increase by 10 m / s 2?

7 question. A skier starts downhill at a speed of 4 m/s. Descent time 30 s. The acceleration is constant and equal to 0.5 m/s 2. What will be the speed at the end of the descent? The car started to slow down at a speed of 20 m/s. What will be the speed of the car after 4 s if it moves with a constant acceleration -2 m / s 2?

Lesson topic: “Rectilinear uniformly accelerated motion.

Problem solving.

The purpose of the lesson: To systematize knowledge about the methods of solving problems with uniformly accelerated motion.

Lesson objectives:

To form the ability to distinguish accelerated movement and characterize it with the help of physical quantities - acceleration, speed.

Learn how to plot speed.

Learn how to write a velocity equation from a velocity graph.

Learn how to write a speed equation.

During the classes.

1. Organizational stage

Greeting, checking the preparedness of students for the lesson, disclosing the objectives of the lesson and its plan.

front poll.

1) What is called acceleration of uniformly accelerated motion?

2) What is uniformly accelerated motion?

3) What characterizes acceleration? What formula is used to calculate? (a x =

4) Under what condition does the modulus of the velocity vector of a moving body increase? Decrease?

5) Write down the formula by which you can calculate the projection of the instantaneous velocity vector

(V x = V 0 x + a x t)

In today's lesson, we will consider the following questions:

How to write a velocity equation;

How to determine the direction of speed and acceleration from the equation of speed;

How to build a velocity projection graph using the velocity equation:

How to write a speed equation from a velocity projection graph.

Task 1. Based on this figure, write the velocity projection equation:

3m/s 2 1m/s 2

1 body: V x \u003d 6 - 3 t, because the velocity vector is co-directed with the X axis, then V 0 x \u003d 6 m / s, the acceleration vector is oppositely directed with the X axis, then a x \u003d -3 m / s 2.

2 body: V x \u003d 2 + t, because the velocity vector is co-directed with the X axis, then V 0 x \u003d 2 m / s, the acceleration vector is also co-directed with the X axis, then a x \u003d 1 m / s 2.

Task 2. (on one's own).

According to the velocity projection equations, draw the position of the bodies on the coordinate line.

V x = -10 + 2 t 2) V x = -6 - 3 t

2m/s 2 3m/s 2

10m/s 6m/s X

Task 3. According to the velocity projection equations, construct velocity projection graphs. (From the condition of the first task)

1) V x = 6 - 3 t 2) V x = 2 + t

The graphs of these functions are straight lines, which are built on points.

Questions for students:

1. How does the first body move? The second body? (the first body slows down, the second accelerates)

2. What does the point of intersection of graphs mean? (the velocities of the bodies after 1 second after the start of movement became equal)

Task4. Based on the velocity projection graph, write the velocity projection equation. (fig A)

(Fig.A)

Answer: according to the schedule, we determine that V 0x \u003d 3m / s. What is the acceleration? a x =

and x \u003d \u003d 2 m / s 2. Substituting the numbers into the equation, we have: V x = 3 +2 t .

Fixing:

Which of the following equations describes the movement in which the speed of the body increases?

Figure 1 shows a graph of the dependence of the speed of the body on time. What is the equation for this graph?

(fig.1)

Which of the graphs (Fig. 2) corresponds to the velocity equation V = 2-t?

(fig.2)

Which of the graphs (Fig. 3) corresponds to the uniformly accelerated movement of the body, in which the acceleration vector is directed opposite to the velocity vector?

(fig.3)

According to the graph of the dependence of speed on time (Fig. 4), determine the acceleration of the body at the time t = 4s.

(Fig. 4)

Results. Homework. §6. Exercise 6 (3.4)

List of used literature

1. Peryshkin A.V., Gutnik E.M. Physics. Grade 9 -M. Bustard 2005.

2. Lukashik V.I., Ivanova E.V. Collection of problems in physics grade 7-9 - M .: Education, 2008.

3. Maron A.E., Maron E.A. Physics. Didactic materials. Grade 9. - M. Bustard. 2008

In this lesson on the topic “Rectilinear uniformly accelerated motion. Acceleration” we will consider non-uniform motion and its features. It will be stated what rectilinear non-uniform motion is and how it differs from uniform motion, the definition of acceleration is considered.

The topic of the lesson is “Uneven rectilinear motion, rectilinear uniformly accelerated motion. Acceleration". To describe such a movement, we introduce an important quantity - acceleration.

In previous lessons, the question of rectilinear uniform motion was discussed, that is, such motion when the speed remains constant. What if the speed changes? In this case, they say that the movement is uneven, that is, the speed varies from point to point. It is important to understand that the speed can increase, then the movement will be accelerated, or decrease (Fig. 1) (in this case we will talk about slow movement).

Rice. 1. Movement with change of speed

In general, the change in speed can be characterized by the amount of decrease or increase in speed.

average speed

When we talk about uneven motion, then, in addition to the concept of "instantaneous speed", which we will often use, the concept of "average speed" also becomes extremely important. Moreover, it is this concept that will allow us to give a correct definition of instantaneous speed.

What is average speed? This can be understood with a simple example. Imagine that you are driving from Moscow to St. Petersburg and drive 700 km in 7 hours. What was your speed during this move? If a car traveled 700 km in 7 hours, then its speed was 100 km/h. But this does not mean that the speedometer at every moment showed 100 km / h, because somewhere the car was in a traffic jam, somewhere it accelerated, somewhere it overtook or even stopped. In this case, we can say that we were looking not for instantaneous speed, but for some other one.

It is for such situations in physics that the concept of average speed (as well as average ground speed) is introduced. Today we will consider both one and the other and find out which one is more convenient and practical to use.

The average speed is the ratio of the module of the total displacement of the body to the time during which this movement is completed: .

Imagine an example: you went shopping and returned home, the module of your displacement is zero, but the speed was not zero, so the concept of average speed is inconvenient in this case.

Let's move on to a more practical concept - the average ground speed. The average ground speed is the ratio of the total path traveled by the body to the total time for which this path has been traveled:.

This concept is convenient, because the path is a scalar value, it can only grow. Often the concepts of average speed and average ground speed are confused, and we will also often mean average ground speed by average speed.

There are many interesting problems for finding the average speed, the most interesting of which we will consider shortly.

Determination of instantaneous speed through the average speed of movement

In order to describe non-uniform motion, we introduce the concept of instantaneous speed, calling it the speed at a given point of the trajectory at a given time. But such a definition will not be correct, because we know only two definitions of speed: the speed of uniform rectilinear motion and the average speed, which we use when we want to find the ratio of the full path to the total time. These definitions do not apply in this case. How to correctly find the instantaneous speed? Here you can use the concept of average speed.

Let's look at the figure, which shows an arbitrary section of a curvilinear trajectory with point A, in which we need to find the instantaneous speed (Fig. 4). To do this, consider a section that contains point A, and draw a displacement vector on this section. The average speed in this section will be the ratio of displacement to time. We will reduce this section and find the average speed in a similar way already for a smaller section. By making the passage to the limit in this way from to, etc., we arrive at a very small displacement in a very small period of time.

Rice. 3. Determination of instantaneous speed through average speed

Of course, at first the average speeds will differ greatly from the instantaneous speed at point A, but the closer we approach point A, the less the conditions of motion will change during this time, the more the motion will resemble uniform motion, for which we know what is speed.

So, when the time interval tends to zero, the average speed practically coincides with the speed at a given point of the trajectory, and we pass to the instantaneous speed. The instantaneous velocity at a given point in the trajectory is the ratio of the small displacement that the body makes to the time it took.

It is interesting that in English there are two separate definitions for the concept of speed: speed (speed module), hence the speedometer; velocity, the first letter of which is v, hence the designation of the velocity vector.

Instantaneous speed has a direction. Recall that when we talked about instantaneous speed, we drew displacements, and so on. (Fig. 4). In relation to the section of the curvilinear trajectory, they are secant. If you get closer to point A, they will become tangent (Fig. 5). The instantaneous velocity on a section of the trajectory is always directed tangentially to the trajectory.

Rice. 4. When the area is reduced, the secants approach the tangent

For example, in the rain, when a passing car splashes us with drops, they fly exactly tangentially to the circle, and this circle is the wheel of the car (Fig. 6).

Rice. 5. Movement of drops

Another example: if a stone is tied to a tourniquet and untwisted, then when the stone comes off, it will also fly tangentially to the trajectory along which the tourniquet moves.

We will consider other examples when studying uniformly accelerated motion.

To characterize the non-uniform motion, a new physical quantity is introduced - instantaneous speed. Instantaneous speed is the speed of a body at a given moment in time or at a given point in the trajectory. A device that shows instantaneous speed is on any vehicle: in a car, train, etc. This is a device called a speedometer (from the English speed - “speed”).

We draw your attention to the fact that instantaneous speed is defined as the ratio of movement to the time during which this movement occurred. If the displacement decreases, tends to a point, then in this case we can talk about instantaneous speed: .

Note that and are body coordinates (Fig. 2). If the time interval is very small, then the change in coordinates will occur very quickly, and the change in speed over a small interval will be imperceptible. We characterize the speed on this interval as instantaneous speed.

Rice. 2. On the question of determining the instantaneous speed

Thus, uneven movement makes sense to characterize the change in speed from point to point, how fast it happens. This change in speed is characterized by a quantity called acceleration. Acceleration is denoted as a vector quantity.

Acceleration is a physical quantity that characterizes the rate of change of speed. In fact, the rate of change of speed is acceleration. Since it is a vector, the acceleration projection value can be negative or positive.

Acceleration is measured in and is found by the formula: . Acceleration is defined as the ratio of the change in speed to the time during which this change has occurred.

An important point is the difference in the velocity vectors. Please note that we will denote the difference (Fig. 3).

Rice. 6. Subtraction of velocity vectors

In conclusion, we note that the projection of acceleration onto the axis, just like any vector quantity, can have negative and positive values ​​depending on the direction. It is important to note that where the change in speed is directed, acceleration will be directed there (Fig. 7). This is of particular importance in curvilinear motion, when not only the value of the speed changes, but also the direction.

Rice. 7. Projection of the acceleration vector on the axis

Bibliography

1. Kikoin I.K., Kikoin A.K. Physics: a textbook for the 9th grade of high school. - M.: Enlightenment.
2. Slobodyanyuk A.I. Physics 10. Part 1. Mechanics. Electricity.
3. Physics. Mechanics. Grade 10 / Ed. Myakisheva G.Ya. - M.: Bustard.
4. Filatov E.N. Physics 9. Part 1. Kinematics. - VSMF: Vanguard.

Homework

1. What is the difference between average speed and instantaneous speed?
2. The cyclist's initial speed is 36 km/h, then he slows down to 18 km/h. He slowed down for 10 seconds. With what acceleration was the cyclist moving and where was it directed?
3. The boy left point B and went to point C, while walking 400 m, and from there returned to point A. What is the average ground speed if the distance from point A to point B is 150 meters, and the boy spent 12 minutes on the whole journey ?

Lesson No. 7/7 on the topic “Rectilinear uniformly accelerated motion. Acceleration"

The stage of setting goals and objectives of the lesson

Educational:

1. to form the concept of rectilinear uniformly accelerated motion, acceleration; consider the main characteristics of uniformly accelerated motion;
2. build graphs of the speed of uniform and equally variable motion;
3. continue the formation of knowledge on the physical foundations of obtaining alternating current.

Developing:

1. to develop the practical skills of students: the ability to analyze, generalize, highlight the main idea from the teacher's story and draw conclusions;
2. develop the ability to apply acquired knowledge in new conditions.

Educators:

1. to broaden the horizons of students about the types of mechanical movement (in particular, about rectilinear equally variable (uniformly accelerated) movement);
2. to develop the skills of educational work in compiling a basic outline (scheme) of the material.

Planned learning outcomes

Metasubject : to master the skills of self-acquisition of knowledge about the rectilinear uniformly accelerated motion of bodies, regulatory UUD in solving computational problems.

Personal : to form a cognitive interest and creative initiative, independence in acquiring new knowledge about the acceleration of the body during rectilinear uneven movement, a value attitude towards each other, towards the teacher, towards learning outcomes; be able to make independent decisions, justify and evaluate the results of their actions.

General subject: conduct observations, plan and conduct an experiment to study rectilinear uniformly accelerated motion; explain the results and draw conclusions; apply theoretical knowledge in practice; solve computational problems to determine acceleration, time, initial and final speeds.

Private subject: explain the physical meaning of the concepts: instantaneous speed, acceleration; give examples of uniformly accelerated motion; write down the formula for determining the acceleration in vector form and in the form of projections on the selected axis; apply the formula for calculating acceleration when solving design problems.

Technical support of the lesson - computer, multimedia projector

1. Organizational stage

2.Motivation for learning activities.

2. Knowledge control

2.1. Individual work on cards

2.2. Frontal survey on the topic "Uniform rectilinear motion"

3. Discovery of new knowledge

With uneven motion, the instantaneous speed of the body changes continuously: from point to point, from one moment of time to another.How to calculate the instantaneous speed of a body?The speed of a body at a given point in time or at a given point in the trajectory is calledinstant speed.

To calculate the displacement of a body at any point in time, it was necessary to know how quickly it changes over time. In the same way, to calculate the speed at any given time, you need to know how fast it changes, or, they say, what is the change in speed per unit time.

For simplicity, we will consider such a rectilinear non-uniform motion of the body, in which its speed changes in the same way for any equal time intervals. Such a movement is calleduniformly accelerated.

If at some initial moment of time the speed of the body is equal to υ 0 , and after a certain period of time it turns out to be equal to υ, then for each unit of time the speed changes by

This value characterizes the rate of change of speed. She is called by acceleration and denoted by the Latin letter a :

Acceleration - a physical vector quantity that characterizes the rate of change in speed and is numerically equal to the ratio of the change in the speed of the body to the time interval during which this change occurred.

In the SI system, acceleration is measured in

Let us determine the direction of the acceleration vector at some point in time. To do this, you need to find the vector of change in the speed of the body. To do this, you need the beginning of the vector υ 0 parallel translation is compatible with the beginning of the vector u. Let's complete the drawing to a triangle. As a result, we obtain the vector of the difference of two vectors. It is directed towards the decreasing vector, in our case, towards the final velocity vector.

Let us consider the relationship between the signs of the projections of velocity and acceleration and the nature of the motion of the body. If athe velocity vector is co-directed with the acceleration vector(i.e. the velocity vector is directed in the same direction as the acceleration vector), thenbody speed increases.

Primary fixation of the material

And so, we will draw the main conclusions:

• Uneven motion is such a motion in which the body, for any equal intervals of time, makes different movements.
• In some cases, when dealing with non-uniform motion, they use the concept of average speed, which shows what the displacement that the body makes on average per unit time is.
• At each point of the trajectory of motion and at each moment of time, the speed of the body has a certain value.
• The speed of a body at a given point in time or at a given point in the trajectory is called the instantaneous speed.

• The direction of the acceleration vector coincides with the direction of the velocity change vector of the body.
• Consider the connection between the signs of velocity projections and acceleration with the nature of the movement of the body.
• If the velocity vector is co-directed with the acceleration vector (i.e., the velocity vector is directed in the same direction as the acceleration vector), then the speed of the body increases.
• If the velocity vector is directed in the direction opposite to the acceleration vector, then the speed of the body decreases.
• And, finally, the body's speed is constant if the acceleration vector is zero or perpendicular to the speed vector.

Problem solving

1. The speed of the paratrooper's descent after opening the parachute decreased from 60 to 5 m/s in 1.1 seconds. Find the parachutist's acceleration.
2. The acceleration of a passenger aircraft during takeoff lasted 25 seconds; by the end of the acceleration, the aircraft had a speed of 216 km/h. Determine the acceleration of the aircraft..
3. The car acquires a speed of 20 m/s after 10 s. With what acceleration was the car moving? After what time will its speed become equal to 108 km/h if it moves with the same acceleration?
4. The body is moving uniformly. How long will it take to move in the same direction as at the initial moment, if v 0x \u003d 20 m / s, and x \u003d - 4 m / s 2?

Reflection.

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Homework§5 questions. Exercise 5 (2,3), 1436

Grade 9 physics Topic: Rectilinear uniformly accelerated motion. Acceleration.

Lesson Objectives:

Educational: repetition, deepening and systematization of information available to students about mechanical phenomena; develop new knowledge and skills:definition of rectilinear equally variable motion, acceleration, unit of acceleration, projections of acceleration.

Developing: development of thinking, emotional-volitional and need-motivational areas; mental activity (perform operations of analysis, synthesis, classification, the ability to observe, draw conclusions,

Educational: formation of a system of views on the world, the ability to follow the norms of behavior.

Lesson type: combined.

Methods: verbal, visual, practical.

Equipment:

Lesson plan.

Organizing time

Repetition (problem solving).

Learning new material.

Homework

Summing up the lesson.

Reflection

During the classes.

Org. Moment.

Repetition.

Problem solving exercise 2 (1 - 3).

1. At the initial moment of time, the body was at a point with coordinatesX 0 = - 2m andat 0 =4m. The body has moved to a point with coordinatesX =2m andat =1m. Find the projection of the displacement vector on the x and y axes. Draw a displacement vector.

2. From the starting point with coordinatesX 0 = - 3m andat 0 \u003d 1m the body has gone some way, so the projection of the displacement vector onto the axisX turned out to be equal to 5.2 m, and on the axisat - 3m. Find the coordinates of the final position of the body. Draw a displacement vector. What is its modulus?

3. The traveler walked 5km south and then another 12km east. What is the modulus of its displacement?

Learning new material.

Presentation "Vectors and actions on them." Let us repeat clearly what vectors are and what actions can be performed on them.

Question: What kind of movement is called uniform?

Answer: A movement in which a body travels equal distances in equal intervals of time.

Movement at a constant speed.

Question: What is called the speed of rectilinear uniform motion?

Answer: A constant vector value equal to the ratio of displacement to the time interval during which this change occurred.

V = s / t .

Question: Then tell me, how do you understand: the speed of the car is 60 km / h?

Answer: Every hour a car travels 60 km.

Question: Is speed a scalar or a vector quantity?

Answer: Scalar. Therefore, it is characterized by direction and modulus (numerical value).

Question: In what cases is the projection of the velocity vector positive, in what cases is it negative?

Answer: It is positive if the projection of the velocity vector is co-directed with the axis.

It is negative if the velocity projection and the selected axis are oppositely directed.

Question: Determine the sign of the velocity vector projection

Answer :1-positive.

2-positive

3-negative

4 is equal to 0

Question: Remember the formula by which you can find the position of the body at any time.

Answer: x = x 0 + v X t

Main material.

Before that, we had to deal with uniform motion. Let's repeat it again.

Uniform motion is a motion in which a body travels equal distances in equal intervals of time. In other words, moving at a constant speed is not very common in practice. Much more often you have to deal with such a movement in which the speed changes with time. Such a movement is called uniform.

With the simplest type of uniformly variable motion is uniformly accelerated. At which the body moves along a straight line, and the projection of the body's velocity vector changes in the same way for any equal time intervals. Suppose a car is moving along the road and gasoline drips from the tank at regular intervals and leaves traces.

Time, every 2sec.

We see that at the same time intervals the speed changes in the same way. So such a movement is called uniformly accelerated.

Teacher: Let's write down in notebooks the definition of uniformly accelerated motion.

The movement of a body in which its speed changes in the same way for any equal intervals of time is called uniformly accelerated.

When considering uniformly accelerated motion, the concept of instantaneous velocity is introduced.

Instantaneous speed is the speed at each specific point of the trajectory, at the corresponding moment in time.

Consider a motion in which at the initial moment of time the speed of the body was equal to V 0 , and after a time interval t it turned out to be equal to V,

then the ratio is the rate of change of velocity.

Those. the rate at which speed changes is called acceleration.

a =

V 0 - initial speed, speed at time t=0

V is the speed that the body had at the end of the interval t.

Acceleration is a vector quantity.

- [a]=m/s 2

From the formula, you can find the value of the speed at a certain moment.

First, we write the speed value in vector form, and then in scalar form.

V= V 0 + at

V= V 0 - at

The acceleration of a body is a quantity that characterizes the rate of change of speed; it is equal to the ratio of the change in speed to the time interval for which this change occurred.

Uniformly accelerated motion is motion with constant acceleration.

Because Acceleration is a vector quantity, so it has a direction.

How to determine where the acceleration vector is directed?

Suppose a body moves in a straight line and its speed increases with time. Let's show it on the drawing.

In this case, the acceleration vector is directed to the same speed as the speed vector.

If the body is moving, and its speed decreases over time (slows down) - the acceleration vector is directed opposite to the velocity vector.

If the velocity and acceleration vectors of a moving body are directed in the same direction, then the modulus of the velocity vectorincreases.

If in opposite directions, then the modulus of the velocity vectordecreases.

Homework

§four ex. 3.

Summarizing.

1. What movement is called uniformly accelerated or equally variable?

2. What is called acceleration?

3. What formula expresses the meaning of acceleration?

4. What is the difference between "accelerated" rectilinear motion and "slow"?

Thus, rectilinear motion is considered of two types: uniform and equally variable (with acceleration). Uniform with constant speed, uniform with constant acceleration. Acceleration characterizes the rate of change of speed.

Reflection.

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