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Rectilinear uniformly accelerated motion acceleration lesson notes. Lesson summary

In this lesson on the topic “Rectilinear uniformly accelerated motion. Acceleration" we will look at uneven motion and its features. It will be explained what rectilinear non-uniform motion is and how it differs from uniform motion, and the definition of acceleration will be 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 issue of rectilinear uniform motion was discussed, i.e., 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 changes 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 motion).

Rice. 1. Movement with changing speed

In general, the change in speed can be characterized by the magnitude of the 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 a car from Moscow to St. Petersburg and travel 700 km in 7 hours. What was your speed during this movement? If a car traveled 700 km in 7 hours, then its speed was 100 km/h. But this does not mean that the speedometer showed 100 km/h at every moment of time, since somewhere the car was stuck in a traffic jam, somewhere it was accelerating, somewhere it was overtaking or even stopping. In this case, we can say that we were not looking for instantaneous speed, but some other one.

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

Average speed is the ratio of the modulus of total movement of a body to the time during which this movement is completed: .

Let's imagine an example: you went out to the store for shopping and returned home, the modulus of your movement is zero, but the speed was not zero, so the concept of average speed in this case is inconvenient.

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

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

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

Determination of instantaneous speed through average speed

In order to describe uneven motion, we introduce the concept of instantaneous speed, calling it the speed at a given point of the trajectory at a given moment in 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 in the case when we want to find the ratio of the total path to the total time. These definitions are not suitable in this case. How to correctly find the instantaneous speed? Here we can use the concept of average speed.

Let's look at the figure, which shows an arbitrary section of a curved trajectory with point A, at 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 in this section. The average speed in this section will be the ratio of displacement to time. We will reduce this section and similarly find the average speed for a smaller section. By thus making the limiting transition from to, etc., we arrive at a very small movement in a very small period of time.

Rice. 3. Determination of instantaneous speed through average speed

Of course, at first the average speeds will be very different from the instantaneous speed at point A, but the closer we get to point A, the less the moving conditions will change during this time, the more the movement will resemble the uniform movement for which we know what is speed?

So, as the time interval tends to zero, the average speed practically coincides with the speed at a given point of the trajectory, and we move on to the instantaneous speed. Instantaneous speed at a given point of the trajectory is the ratio of the small movement that the body makes to the time during which it occurred.

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

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

Rice. 4. As the area decreases, the secants approach the tangent

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

Rice. 5. Movement of drops

Another example: if you tie a stone to a rope and spin it, then when the stone comes off, it will also fly tangentially to the path along which the rope is moving.

We will consider other examples when studying uniformly accelerated motion.

To characterize uneven 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 found on any vehicle: in a car, train, etc. This is a device called a speedometer (from the English speed - “speed”).

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

Please note that and are the coordinates of the body (Fig. 2). If the time period is very short, then the change in coordinates will occur very quickly, and the change in speed over a short period will be imperceptible. We characterize the speed over a given interval as instantaneous speed.

Rice. 2. On the issue of determining instantaneous speed

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

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

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

An important point is the difference in 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 wherever the change in speed is directed, the acceleration will be directed (Fig. 7). This is of particular importance during curvilinear movement, when not only the speed value changes, but also the direction.

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

Bibliography

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

Homework

What is the difference between average speed and instantaneous speed?
The cyclist's initial speed is 36 km/h, then he slows down to 18 km/h. He braked for 10 seconds. With what acceleration was the cyclist moving and where was it directed?
The boy left point B and headed to point C, having walked 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? ?

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Summary of a physics lesson in 8th grade on the topic "Rectilinear uniformly accelerated motion. Acceleration."

Lesson developed and sent by: Kalinin V.N., student of Belinsky State Pedagogical University

Lesson summary.

Lesson topic: Rectilinear uniformly accelerated motion. Acceleration.

Lesson objectives: Introduce students to the uniformly alternating type of motion. Introduce the concept of acceleration, instantaneous speed.

During the classes.

Lesson steps:

1.Org.moment
2.Repetition. Frontal survey
3. Studying a new topic. Conversation, story
4. Consolidation of the studied material. Conversation
5.D/Z

1. Write on the board

1.Repetition.Checking homework.

Teacher: We finished the last lesson by solving a problem in which, using a graph of coordinates versus time, we found the place and time of meeting of cars. At home it was necessary to check the results obtained analytically.

Teacher: Well, did the answers agree?

Teacher: Fine! Let's solve one more problem.

Task. The movements of 2 cyclists are given by the equations

Find a meeting time and place for cyclists. (I call the student to the board)

Teacher: Let's write down the given first. Now let's remember what a graph of coordinates versus time is.

Students: Straight

Teacher: Fine. Then tell me, how many points are enough to construct a straight line?

9th grade physics Topic: Rectilinear uniformly accelerated motion. Acceleration.

Lesson objectives:

Educational: repetition, deepening and systematization of information about mechanical phenomena available to students; develop new knowledge and skills:definition of rectilinear uniformly alternating motion, acceleration, unit of measurement of acceleration, projection of acceleration.

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

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

Solving problems 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 projections of the displacement vector on the x and y axes. Draw the displacement vector.

2. From the starting point with coordinatesX 0 = - 3m andat 0 =1m the body has traveled some distance, 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 the displacement vector. What is its modulus?

3. The traveler walked 5 km in a southerly direction, and then another 12 km in an easterly direction. What is the magnitude of the movement he made?

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 motion is called uniform?

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

Movement at constant speed.

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

Answer: A constant vector quantity equal to the ratio of the movement to the period of time 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 velocity a scalar or a vector quantity?

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

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

Answer: Positive if the projection of the velocity vector is codirectional with the axis.

Negative if the velocity projection and the selected axis are in opposite directions.

Question: Determine the sign of the velocity vector projection

Answer :1-positive

2-positive

3-negative

4- equals 0

Question: Remember the formula that can be used to find the position of the body at any time.

Answer: x = x 0 + v X t

Main material.

Before this 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 any equal intervals of time. In other words, movement at a constant speed is not very common in practice. Much more often you have to deal with a movement in which the speed changes over time. This kind of motion is called uniformly variable.

The simplest type of uniformly alternating motion is uniformly accelerated. In which the body moves along a straight line, and the projection of the body’s velocity vector changes equally over any equal periods of time. Let's say a car is moving along the road and gasoline drips from the tank at regular intervals and leaves traces.

Time, every 2 sec.

We see that at equal intervals the speed changes equally. So this kind of motion is called uniformly accelerated.

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

The motion of a body in which its speed changes equally over any equal periods of time is called uniformly accelerated.

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

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

Let us consider a movement in which at the initial moment of time the speed of the body was equal to V 0 , and after a period of time t it turned out to be equal to V,

then the ratio is the rate of change of speed.

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 speed value 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 in speed; it is equal to the ratio of the change in speed to the period of time during which this change occurred.

Uniformly accelerated motion is motion with constant acceleration.

Because Acceleration is a vector quantity, which means it has a direction.

How to determine where the acceleration vector is directed?

Let's say a body moves in a straight line and its speed increases over time. Let's depict this in the drawing.

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

If a 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 one direction, then the magnitude of the velocity vectorincreases.

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

Homework

§4 ex. 3.

Summarizing.

1. What kind of motion is called uniformly accelerated or uniformly variable?

2. What is acceleration called?

3. What formula expresses the meaning of acceleration?

4. How does “accelerated” linear motion differ from “slow” motion?

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

Reflection.

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