Lesson on the topic uneven motion and instantaneous speed. Lesson summary: Solving problems "Average speed with uneven movement"

Subject. Uneven movement. average speed

Purpose of the lesson: to familiarize students with the simplest cases of uneven motion

Lesson type: combined

Lesson Plan

LEARNING NEW MATERIAL

Uniform linear motion occurs relatively rarely. Bodies move uniformly and rectilinearly only on small sections of their trajectory, and in other sections their speed changes.

Ø Movement with variable speed, when a body travels different paths over equal periods of time, is called uneven.

To characterize the speed of uneven movement, average and instantaneous speeds are used.

Since the speed in the case of uneven movement changes over time, the formula for calculating the movement cannot be used, because the speed is a variable quantity, and it is not known which value should be substituted into this formula.

However, in some cases, displacement can be calculated by entering a value called average speed. It shows how much movement a body makes on average per unit of time, i.e.

This formula describes the so-called average vector speed. However, it is not always suitable for describing movement. Consider this example: a regular bus left the garage and returned back at the end of the shift. The speedometer shows that the car has traveled 600 km. What is the average driving speed?

Correct answer: the average vector velocity is zero, since the bus returned to the starting point, that is, the displacement of the body is zero.

In practice, the so-called average ground speed is often used, which is equal to the ratio of the distance traveled by the body to the time of movement:

Since the path is a scalar quantity, then the average ground speed (as opposed to the average speed) is a scalar quantity.

Knowing the average speed does not make it possible to determine the position of the body at any time, even if the trajectory of its movement is known. However, this concept is convenient for performing some calculations, for example, calculating travel time.

If you observe the speedometer readings of a car that is moving, you will notice that they change over time. This is especially noticeable during acceleration and braking.

When they say that the speed of a body changes, they mean instantaneous speed, that is, the speed of the body at a certain moment and at a certain point in the trajectory.

Ø Instantaneous speed is a quantity that is equal to the ratio of a very small movement to the period of time during which this movement occurred:

Instantaneous speed is the average speed measured over an infinitesimal period of time.

Question for students while presenting new material

1. The car traveled 60 km per hour. Can we say that his movement was uniform?

2. Why can’t we talk about the average speed of variable movement in general, but can we only talk about the average speed over a certain period of time or about the average speed on a separate section of the route?

3. While driving a car, speedometer readings were taken every minute. Is it possible to calculate the average speed of a car from these data?

4. The average speed over a certain period of time is known. Is it possible to calculate the displacement made during half of this interval?

CONSTRUCTION OF LEARNED MATERIAL

1. The skier covered the first section of the path, 12 m long, in 2 minutes, the second, 3 m long, in 0.5 minutes. Calculate the average ground speed of the skier.

2. A man walked along a straight road 3 km in 1 hour, then returned at a right angle and walked another 4 km in 1 hour. Calculate the average and average ground speed at the first stage of movement, at the second stage and for the entire time of movement.

3. A man traveled the first half of the journey by car at a speed of 7 km/h, and the second half by bicycle at a speed of 2 km/h. Calculate the average ground speed for the entire journey.

4. A pedestrian walked two thirds of the time at a speed of 3 km/h, the rest of the time at a speed of 6 km/h. Calculate the average and average ground speed of the pedestrian.

5. A material point moves along a circular arc with a radius of 4 m, describing a trajectory that is half of the circular arc. In this case, the point moves for the first quarter of the circle at a speed of 2 m/s, and for the second quarter at a speed of 8 m/s. Calculate the average ground speed and average vector speed for the entire time of movement.

Develop students’ thinking abilities, the ability to analyze, identify common and distinctive properties; develop the ability to apply theoretical knowledge in practice when solving problems of finding the average speed of uneven movement.

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Lesson in 9th grade on the topic: “Average and instantaneous speeds of uneven motion”

Teacher – Malyshev M.E.

Date -10/17/2013

Lesson objectives:

Educational goal:

Repeat the concept - average and instantaneous speeds,
learn to find the average speed under various conditions, using problems from the materials of the State Examination and Unified State Examination of previous years.

Developmental goal:

develop students’ thinking abilities, the ability to analyze, identify common and distinctive properties; develop the ability to apply theoretical knowledge in practice; develop memory, attention, observation.

Educational goal:

to cultivate a sustainable interest in the study of mathematics and physics through the implementation of interdisciplinary connections;

Lesson type:

a lesson in generalizing and systematizing knowledge and skills on this topic.

Equipment:

computer, multimedia projector;
notebooks;
set of L-micro equipment for the “Mechanics” section

During the classes

1. Organizational moment

Mutual greeting; checking students' readiness for the lesson, organizing attention.

2. Communicating the topic and objectives of the lesson

Slide on screen: “Practice is born only from a close combination of physics and mathematics" Bacon F.

The topic and objectives of the lesson are reported.

3. Incoming control (repetition of theoretical material)(10 min)

Organization of oral frontal work with the class on repetition.

Physics teacher:

1. What is the simplest type of movement you know? (uniform movement)

2. How to find speed with uniform motion? (displacement divided by time v= s/t )? Uniform movement is rare.

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.

3. How to find speed with uneven movement? What is it called? (Average speed, vср = s/t)

In practice, when determining the average speed, a value equal tothe ratio of the path s to the time t during which this path is covered: v av = s/t . She is often calledaverage ground speed.

4. What features does average speed have? (Average speed is a vector quantity. To determine the magnitude of the average speed 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).

5. What is instantaneous speed? What is the direction of the instantaneous velocity vector? (Instantaneous speed is the speed of a body at a given moment of time or at a given point on the trajectory. The vector of instantaneous speed at each point coincides with the direction of movement at a given point.)

6. How does instantaneous speed during uniform rectilinear motion differ from instantaneous speed during uneven motion? (In the case of uniform rectilinear motion, the instantaneous speed at any point and at any time is the same; in the case of uneven rectilinear motion, the instantaneous speed is different).

7. Is it possible to determine the position of a body at any moment in time knowing the average speed of its movement on any part of the trajectory? (its position cannot be determined at any time).

Suppose that a car travels 300 km in 6 hours. What is the average speed? The average speed of a 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. of time.”

1. Orally find the speed of the car if it covered a distance of 180 km in 3 hours.

2. The car drove for 1 hour at a speed of 80 km/h and for 1 hour at a speed of 60 km/h. Find the average speed. Indeed, the average speed is (80+60)/2=70 km/h. In this case, the average speed is equal to the arithmetic mean of the speeds.

3. Let's change the condition. The car drove for 2 hours at a speed of 60 km/h and for 3 hours at a speed of 80 km/h. What is the average speed along the entire journey?

(60 2+80 3)/5=72 km/h. Tell me, is the average speed now equal to the arithmetic mean of the speeds? No.

The most important thing to remember when finding the average speed is that it is an average, not an arithmetic mean speed. Of course, having heard the problem, you immediately want to add the speeds and divide by 2. This is the most common mistake.

The average speed is equal to the arithmetic mean of the speeds of the body during movement only in the case when the body with these speeds travels the entire path in equal periods of time.

4. Problem solving (15 min)

Task No. 1. The speed of the boat along the current is 24 km per hour, against the current 16 km per hour. Find the average speed.(Checking the completion of tasks at the board.)

Solution. Let S be the path from the starting point to the final point, then the time spent on the path along the current is S/24, and against the current is S/16, the total time of movement is 5S/48. Since the entire journey, there and back, is 2S, therefore, the average speed is 2S/(5S/48) = 19.2 km per hour.

Experimental study“Uniformly accelerated motion, initial speed equal to zero”(The experiment is carried out by students)

Before we begin practical work, let’s remember the safety rules:

Before starting work: carefully study the content and procedure for conducting a laboratory workshop, prepare the workplace and remove foreign objects, place instruments and equipment in such a way as to prevent them from falling and tipping over, check the serviceability of the equipment and instruments.
During work : accurately follow all the teacher’s instructions, do not carry out any work independently without his permission, monitor the serviceability of all fastenings in devices and fixtures.
Upon completion of work: tidy up the workplace, hand over instruments and equipment to the teacher.

Study of the dependence of speed on time during uniformly accelerated motion (initial speed is zero).

Target: study of uniformly accelerated motion, plotting the v=at dependence based on experimental data.

From the definition of acceleration it follows that the speed of the body v, moving rectilinearly with constant acceleration, after some time tafter the start of movement can be determined from the equation: v= v 0 +аt . If the body begins to move without having an initial speed, that is, when v0 = 0, this equation becomes simpler: v= a t. (1)

The speed at a given point on the trajectory can be determined by knowing the movement of the body from rest to this point and the time of movement. Indeed, when moving from a state of rest ( v 0 = 0 ) with constant acceleration the displacement is determined by the formula S= at 2 /2, from where, a=2S/ t 2 (2). After substituting formula (2) into (1):v=2 S/t (3)

To perform the work, the guide rail is installed using a tripod in an inclined position.

Its upper edge should be at a height of 18-20 cm from the table surface. Place a plastic mat under the bottom edge. The carriage is installed on the guide in the uppermost position, with its protrusion with the magnet facing the sensors. The first sensor is placed near the carriage magnet so that it starts the stopwatch as soon as the carriage starts moving. The second sensor is installed at a distance of 20-25 cm from the first. Further work is performed in this order:

Measure the movement that the carriage will make when moving between the sensors - S 1
The carriage is started and the time of its movement between the sensors t is measured 1
Using formula (3), the speed at which the carriage moved at the end of the first section v is determined 1 =2S 1 /t 1
Increase the distance between the sensors by 5 cm and repeat a series of experiments to measure the speed of the body at the end of the second section: v 2 =2 S 2 /t 2 In this series of experiments, as in the first, the carriage is launched from its highest position.
Two more series of experiments are carried out, increasing the distance between the sensors by 5 cm in each series. This is how the velocity values v are foundз and v 4
Based on the data obtained, a graph of the dependence of speed on movement time is constructed.
Summing up the lesson

Homework with comments:Select any three tasks:

1. A cyclist, having traveled 4 km at a speed of 12 km/h, stopped and rested for 40 minutes. He drove the remaining 8 km at a speed of 8 km/h. Find the average speed (in km/h) of the cyclist for the entire journey?

2. A cyclist traveled 35 m in the first 5 s, 100 m in the next 10 s, and 25 m in the last 5 s. Find the average speed along the entire path.

3. The first 3/4 of the time the train moved at a speed of 80 km/h, the rest of the time - at a speed of 40 km/h. What is the average speed (in km/h) of the train along the entire journey?

4. The car covered the first half of the journey at a speed of 40 km/h, and the second half at a speed of 60 km/h. Find the average speed (in km/h) of the car along the entire journey?

5. The car drove the first half of the journey at a speed of 60 km/h. He drove the rest of the way at a speed of 35 km/h, and the last part at a speed of 45 km/h. Find the average speed (in km/h) of the car along the entire journey.

“Practice is born only from the close combination of physics and mathematics” Bacon F.

a) “Acceleration” (initial speed is less than final speed) b) “Braking” (final speed is less than initial speed)

Orally 1. Find the speed of the car if it covered a distance of 180 km in 3 hours. 2. The car drove for 1 hour at a speed of 80 km/h and for 1 hour at a speed of 60 km/h. Find the average speed. Indeed, the average speed is (80+60)/2=70 km/h. In this case, the average speed is equal to the arithmetic mean of the speeds. 3. Let's change the condition. The car drove for 2 hours at a speed of 60 km/h and for 3 hours at a speed of 80 km/h. What is the average speed along the entire journey?

(60* 2+80* 3)/5=72 km/h. Tell me, is the average speed now equal to the arithmetic mean of the speeds?

Problem The speed of the boat downstream is 24 km per hour, against the current is 16 km per hour. Find the average speed of the boat.

Solution. V av = 2s / t 1 + t 2 t 1 = s / V 1 and t 2 = s / V 2 V av = 2s / V 1 + s / V 2 = 2 V 1 V 2 / V 1 + V 2 V avg = 19.2 km/h

Take home: 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 kilometers per hour.

Preparing for cancer. Physics.
Abstract 2. Uneven movement.

5. Uniformly variable (uniformly accelerated) motion

Uneven movement– movement with variable speed.
Definition. Instantaneous speed– the speed of the body at a given point of the trajectory, at a given moment in time. It is found by the ratio of the movement of the body to the time interval ∆t during which this movement was made, if the time interval tends to zero.

Definition. Acceleration – a value showing how much the speed changes over the time interval ∆t.

Where is the final, and is the initial speed for the considered time interval.

Definition. Uniformly alternating linear motion (uniformly accelerated)- this is a movement in which, over any equal periods of time, the speed of the body changes by an equal value, i.e. This is motion with constant acceleration.

Comment. When we say that the motion is uniformly accelerated, we assume that the speed increases, i.e. projection of acceleration when moving along the reference direction (speed and acceleration coincide in direction), and speaking equally slow, we assume that the speed decreases, i.e. (speed and acceleration are directed towards each other). In school physics, both of these movements are usually called uniformly accelerated.

Displacement equations, m:

Graphs of uniformly variable (uniformly accelerated) rectilinear motion:

A graph is a straight line parallel to the time axis.

A graph is a straight line that is built point by point.

Comment. The speed graph always starts with the initial speed.

The topic of the lesson is “Uniform and uneven movement. Speed"

Lesson objectives:

Educational:

introduce the concepts of uniform and uneven
movement;
introduce the concept of speed as physical
quantities, formula and units of measurement.

Educational:

develop cognitive interests,
intellectual and creative abilities,
interest in studying physics;

Developmental:

develop independent skills
acquisition of knowledge, organization of educational
activities, goal setting, planning;
develop the ability to systematize,
classify and summarize the acquired knowledge;
develop communication skills
students

During the classes:

1. Repetition

What is mechanical movement? Give examples

What is a trajectory? What are they?

What is a path? How is it designated, in what units is it measured?

Translate:

in m 80 cm, 5 cm, 2 km, 3 dm, 12 dm, 1350 cm, 25000 mm, 67 km

in cm 2 dm, 5 km, 30 mm

2. Assimilation of new knowledge

Uniform movement-motion in which a body travels equal distances in any equal intervals of time.

Uneven movement- a movement in which a body travels unequal paths over any equal intervals of time.

Examples of uniform and uneven movement

Speed of linear uniform motion- a physical quantity equal to the ratio of the path to the time during which the path was traveled.

Let's check if our knowledge is enough to solve the following problem. Two cars started moving simultaneously from the village at the same speed of 60 km/h. Can we say that in an hour they will be in the same place?

Conclusion: speed must be characterized not only by number, but also by direction. Such quantities that, in addition to a numerical value, also have a direction are called vector quantities.

Speed is a vector physical quantity.

Scalar quantities are those quantities that are characterized only by a numerical value (for example, path, time, length, etc.)

To characterize uneven motion, the concept of average speed is introduced.

To determine the average speed of a body during uneven movement, the entire distance traveled must be divided by the entire time of movement:

Working with the textbook table p.37

3. Testing the assimilation of new knowledge

Problem solving

1. Convert speed units to basic SI units:

36 km/h = ___________________________________________________________________

120 m/min = ________________________________________________________________

18 km/h = ___________________________________________________________________

90 m/min = ___________________________________________________________________

2. A balloon is moving east at a speed of 30 km/h. Graphically depict the velocity vector using the scale: 1 cm = 10 km/h

Algorithm for solving problems in physics:

1. Read the problem statement carefully and understand the main question; imagine the processes and phenomena described in the problem statement.

2. Re-read the contents of the problem in order to clearly present the main question of the problem, the purpose of its solution, known quantities, based on which you can search for a solution.

3. Briefly write down the conditions of the problem using generally accepted letter notations.

4. Complete a drawing or drawing for the problem.

5. Determine what method will be used to solve the problem; make a plan to solve it.

6. Write down the basic equations that describe the processes proposed by the problem system.

7. Write down the solution in general form, expressing the required quantities in terms of the given ones.

8. Check the correctness of the solution to the problem in general form by performing actions with the names of quantities.

9. Perform calculations with the specified accuracy.

10. Assess the reality of the resulting solution.

11. Write the answer in the required form

3. Find the speed of the French athlete Roman Zaballo, who in 1981 ran the distance between the French cities of Florence and Montpellier (510 km) in 60 hours.

4.Find the speed of a cheetah (the fastest of mammals) if it runs 210 meters in 7 seconds.

5. V.I.Lukashik problems No. 117,118,119

6. Homework: §14,15, exercise 4(4)