t=S:V

15:3 = 5 (s)

Let's make an expression: 5 3: 3 \u003d 5 (s) Answer: 5 s will be required for a horsefly.

Solve the problem.

1. The boat, moving at a speed of 32 km / h, traveled between the piers in 2 hours. How long will it take to go the same way on a boat if it moves at a speed of 8 km / h?

2. A cyclist, moving at a speed of 10 km / h, traveled a distance between villages in 4 hours.

How long does it take for a pedestrian to walk the same path if he is moving at a speed of 15 km/h?

Compound tasks for time. II type.

Sample:

The centipede first ran for 3 minutes at a speed of 2 dm/m, and then it ran at a speed of 3 dm/m. How long did it take the centipede to run the rest of the way if it ran 15 dm in total? We reason like this. This is a task to move in one direction. Let's make a table. We write the words "speed", "time", "distance" in the table with a green pen.

Speed ​​(V) Time (t) Distance (S)

C. - 2 dm / min 3 min? dm

P.-3 dm / min? ? min?dm 15dm

Let's make a plan to solve this problem. To find out the time of the centipede later, you need to find out how far it ran then, and for this you need to know how much distance it ran first.

t p S p S s

S c \u003d V c t

2 3 \u003d 6 (m) - the distance that the centipede ran first.

S p \u003d S - S with

15 - 6 \u003d 9 (m) - the distance that the centipede then ran.

To find the time, you need to divide the distance by the speed.

9:3=3(min)

Answer: in 3 minutes the centipede ran the rest of the way.

Solve the problem.

1. The wolf ran through the forest for 3 hours at a speed of 8 km/h. He ran across the field at a speed of 10 km / h. How long did the wolf run across the field if he ran 44 km?

2. The crayfish crawled to the snag for 3 minutes at a speed of 18 m / min. The rest of the way he crawled at a speed of 16 m / min. How long did it take for the rest of the way for the crab if it crawled 118m?

3. Gena ran to the football field in 48 seconds at a speed of 6 m/s, and then he ran to the school at a speed of 7 m/s. How long will Gena run to school if he ran 477 m?

4. The pedestrian walked to the stop for 3 hours at a speed of 5 km/h, after stopping he walked at a speed of 4 km/h. How long was the pedestrian on the way after stopping, if he passed 23 km?

5. He swam to the snag for 10s at a speed of 8 dm/s, and then he swam to the shore at a speed of 6 dm/s. How long did it take to swim to the shore if he swam 122dm?

Compound tasks for speed. I type

Sample:

Two hedgehogs ran out of the mink. One ran for 6 s at a speed of 2 m/s. How fast must another hedgehog run to cover this distance in 3 seconds? We reason like this. This is a task to move in one direction. Let's make a table. We write the words "speed", "time", "distance" in the table with a green pen.

Speed ​​(V) Time (1) Distance (8)

I - 2 m/s 6 s the same

II - ?m/s 3 s

Let's make a plan to solve this problem. To find the speed of the second hedgehog, you need to find the distance that the first hedgehog ran.

To find the distance, you need to multiply the speed by the time.

S = V I t I

2 6 \u003d 12 (m) - the distance that the first hedgehog ran.

To find the speed, you need to divide the distance by the time.

V II \u003d S: t II

12:3 = 4(m/s)

Let's make an expression: 2 6:3 = 4 (m/s)

Answer; 4m/s speed of the second hedgehog.

Solve the problem.

1. One squid swam for 4 s at a speed of 10 m/s. How fast must another squid swim to cover this distance in 5 s?

2. A tractor, moving at a speed of 9 km/h, traveled between villages in 2 hours. How fast should a pedestrian walk to cover this distance in 3 hours?

3. A bus, moving at a speed of 64 km/h, traveled between cities in 2 hours. How fast should a cyclist travel to cover this distance in 8 hours?

4. The black swift flew for 4 minutes at a speed of 3 km / min. How fast must a mallard duck fly to cover this distance in 6 minutes?

Compound tasks for speed. II type

The skier traveled to the hill for 2 hours at a speed of 15 km / h, and then he rode through the forest for another 3 hours. At what speed will the skier go through the forest if he traveled 66 km in total?

In the proposed task, we are asked to explain how to find the speed, time and distance in the problem. Problems with such values ​​are referred to as motion problems.

Tasks for movement

In total, three basic quantities are used in motion problems, as a rule, one of which is unknown and must be found. This can be done using formulas:

• Speed. The speed in the problem is called a value that indicates how far an object has traveled in units of time. Therefore, it is given by the formula:

speed = distance / time.

• Time. Time in the problem is a value that shows how much time an object spent on the path at a certain speed. Accordingly, it is given by the formula:

time = distance / speed.

• Distance. A distance or path in the problem is a value that shows how far a subject has traveled at a certain speed over a certain period of time. Thus, it is found by the formula:

distance = speed * time.

Outcome

So let's sum it up. Movement tasks can be solved using the above formulas. Jobs can also have multiple moving objects or multiple segments of the path and time. In this case, the solution will consist of several segments, which are eventually added or subtracted depending on the conditions.

let's school lesson turn physics into exciting game! In this article, our heroine will be the formula "Speed, time, distance." We will analyze each parameter separately, give interesting examples.

Speed

What is "speed"? You can watch one car go faster, another slower; one man going fast step, the other - not in a hurry. Cyclists also travel at different speeds. Yes! It's the speed. What is meant by it? Of course, the distance that a person has traveled. the car drove for some Let's say that 5 km / h. That is, in 1 hour he walked 5 kilometers.

The path (distance) formula is the product of speed and time. Of course, the most convenient and accessible parameter is time. Everyone has a watch. Pedestrian speed is not strictly 5 km/h, but approximately. Therefore, there may be an error here. In this case, you'd better take a map of the area. Pay attention to what scale. It should indicate how many kilometers or meters are in 1 cm. Attach a ruler and measure the length. For example, from home to music school straight road. The segment turned out to be 5 cm. And on the scale it is indicated 1 cm = 200 m. This means that the real distance is 200 * 5 = 1000 m = 1 km. How long do you cover this distance? In half an hour? Speaking technical language, 30 min = 0.5 h = (1/2) h. If we solve the problem, it turns out that you are walking at a speed of 2 km / h. The formula "speed, time, distance" will always help you solve the problem.

Don't miss out!

I advise you not to miss out important points. When you are given a task, look carefully in what units of measurement the parameters are given. The author of the problem can cheat. Will write in given:

A man cycled 2 kilometers on a sidewalk in 15 minutes. Do not rush to immediately solve the problem according to the formula, otherwise you will get nonsense, and the teacher will not count it for you. Remember that in no case should you do this: 2 km / 15 min. Your unit of measurement will be km/min, not km/h. You need to achieve the latter. Convert minutes to hours. How to do it? 15 minutes is 1/4 hour or 0.25 hours. Now you can safely 2km/0.25h=8 km/h. Now the problem is solved correctly.

That's how easy it is to remember the formula "speed, time, distance". Just follow all the rules of mathematics, pay attention to the units of measurement in the problem. If there are nuances, as in the example discussed just above, immediately convert to the SI system of units, as expected.

Velocity is a function of time and is defined as absolute value, as well as direction. Often in physics problems it is required to find the initial speed (its magnitude and direction), which the object under study had at the zero moment of time. To calculate initial speed can be used various equations. Based on the data provided in the problem statement, you can choose the most appropriate formula that will make it easy to get the answer you are looking for.

Steps

Finding the initial speed from the final speed, acceleration and time

1. When deciding physical task you need to know which formula you need. To do this, the first step is to write down all the data given in the condition of the problem. If the final speed, acceleration and time are known, it is convenient to use the following relation to determine the initial speed:

   • V i \u003d V f - (a * t)
   • • Vi- starting speed
     • V f- final speed
     • a- acceleration
     • t- time
   • Please note that this standard formula, used to calculate the initial speed.

2. After writing out all the initial data and writing necessary equation, you can substitute into it known quantities. It is important to carefully study the condition of the problem and accurately record each step in solving it.

   • If you make a mistake somewhere, you can easily find it by looking at your notes.

3. Solve the equation. Substituting into the formula known values, use the standard transformations to get the desired result. If possible, use a calculator to reduce the chance of miscalculations.

   • Suppose an object moving east at 10 meters per second squared for 12 seconds accelerates to a terminal velocity of 200 meters per second. We need to find the initial speed of the object.
     • Let's write the initial data:
     • Vi = ?, V f= 200 m/s, a\u003d 10 m / s 2, t= 12 s
   • Multiply the acceleration by the time: a*t = 10 * 12 =120
   • Subtract the resulting value from the final speed: V i \u003d V f - (a * t) = 200 – 120 = 80 Vi= 80 m/s east
   • m/s

   Finding the initial speed from the distance traveled, time and acceleration

   1. Use the right formula. When solving any physical problem, it is necessary to choose the appropriate equation. To do this, the first step is to write down all the data given in the condition of the problem. If the distance traveled, time and acceleration are known, the following relationship can be used to determine the initial speed:

      • This formula includes the following quantities:
        • Vi- starting speed
        • d- distance traveled
        • a- acceleration
        • t- time

   2. Plug in the known quantities into the formula.

      • If you make a mistake in a solution, you can easily find it by reviewing your notes.

   3. Solve the equation. Substituting known values ​​into the formula, use standard transformations to find the answer. If possible, use a calculator to reduce the chance of miscalculations.

      • Let's say an object is moving in westbound with an acceleration of 7 meters per second squared for 30 seconds, while passing 150 meters. It is necessary to calculate its initial speed.
        • Let's write the initial data:
        • Vi = ?, d= 150 m, a\u003d 7 m / s 2, t= 30 s
      • Multiply the acceleration by the time: a*t = 7 * 30 = 210
      • Let's divide it into two: (a * t) / 2 = 210 / 2 = 105
      • Divide the distance by the time: d/t = 150 / 30 = 5
      • Subtract the first value from the second: V i = (d / t) - [(a * t) / 2] = 5 – 105 = -100 Vi= -100 m/s west
      • Write your answer in right way. It is necessary to specify the units of measurement, in our case meters per second, or m/s, as well as the direction of movement of the object. If you do not specify a direction, the answer will be incomplete, containing only the speed value without information about the direction in which the object is moving.

   Finding the initial speed from the final speed, acceleration and distance traveled

   1. Use the appropriate equation. To solve a physical problem, you must choose the appropriate formula. The first step is to write down all the initial data specified in the condition of the problem. If the final speed, acceleration and distance traveled are known, it is convenient to use the following relation to determine the initial speed:

      • V i = √
      • This formula contains the following quantities:
        • Vi- starting speed
        • V f- final speed
        • a- acceleration
        • d- distance traveled

   2. Plug in the known quantities into the formula. After you have written out all the initial data and written down the necessary equation, you can substitute known quantities into it. It is important to carefully study the condition of the problem and accurately record each step in solving it.

      • If you make a mistake somewhere, you can easily find it by looking at the solution.

   3. Solve the equation. Substituting known values ​​into the formula, use the necessary transformations to get the answer. If possible, use a calculator to reduce the chance of miscalculations.

      • Suppose an object is moving north with an acceleration of 5 meters per second squared, and after traveling 10 meters, has a final velocity of 12 meters per second. We need to find its initial speed.
        • Let's write the initial data:
        • Vi = ?, V f= 12 m/s, a\u003d 5 m / s 2, d= 10 m
      • Let's square the final speed: V f 2= 12 2 = 144
      • Multiply the acceleration by the distance traveled and by 2: 2*a*d = 2 * 5 * 10 = 100
      • Subtract the result of the multiplication from the square of the final speed: V f 2 - (2 * a * d) = 144 – 100 = 44
      • Extract Square root from the received value: = √ = √44 = 6,633 Vi= 6.633 m/s northbound
      • Write your answer in the correct form. You must specify the units of measurement, i.e. meters per second, or m/s, as well as the direction of movement of the object. If you do not specify a direction, the answer will be incomplete, containing only the speed value without information about the direction in which the object is moving.

How to solve motion problems? The formula for the relationship between speed, time and distance. Tasks and solutions.

The formula for the dependence of time, speed and distance for grade 4: how is speed, time, distance indicated?

People, animals or cars can move at a certain speed. Per certain time they can go a certain way. For example: today you can walk to your school in half an hour. You walk at a certain speed and cover 1000 meters in 30 minutes. The path that is overcome is denoted in mathematics by the letter S. The speed is indicated by the letter v. And the time for which the path was traveled is indicated by the letter t.

• Path - S
• Speed ​​- v
• Time - t

If you are late for school, you can walk the same path in 20 minutes by increasing your speed. This means that the same path can be traveled in different time and at different speeds.

How does travel time depend on speed?

How more speed, the faster the distance will be covered. And the lower the speed, the more time it will take to complete the path.

How to find the time, knowing the speed and distance?

In order to find the time it took to complete the path, you need to know the distance and speed. If you divide the distance by the speed, you will know the time. An example of such a task:

Problem about the Hare. The hare ran away from the Wolf at a speed of 1 kilometer per minute. He ran 3 kilometers to his hole. How long did it take the hare to reach the hole?

How easy is it to solve motion problems where you need to find distance, time or speed?

1. Read the problem carefully and determine what is known from the condition of the problem.
2. Write this information on a draft.
3. Also write what is unknown and what needs to be found
4. Use the formula for problems about distance, time and speed
5. Enter known data into the formula and solve the problem

Solution for the problem about the Hare and the Wolf.

• From the condition of the problem, we determine that we know the speed and distance.
• Also, from the condition of the problem, we determine that we need to find the time that the hare needed to run to the hole.

We write this data in a draft, for example:

Time is unknown

Now let's write the same with mathematical signs:

S - 3 kilometers

V - 1 km / min

t-?

We recall and write down in a notebook the formula for finding time:

t=S:v

t = 3: 1 = 3 minutes

How to find speed if time and distance are known?

In order to find the speed, if you know the time and distance, you need to divide the distance by the time. An example of such a task:

The hare ran away from the Wolf and ran 3 kilometers to his hole. He covered this distance in 3 minutes. How fast was the rabbit running?

The solution to the problem of movement:

1. We write down in the draft that we know the distance and time.
2. From the condition of the problem, we determine that we need to find the speed
3. Remember the formula for finding speed.

Formulas for solving such problems are shown in the picture below.

Formulas for solving problems about distance, time and speed

We substitute the known data and solve the problem:

Distance to the burrow - 3 kilometers

The time for which the Hare ran to the hole - 3 minutes

Speed ​​- unknown

Let's write down these known data with mathematical signs

S - 3 kilometers

t - 3 minutes

v-?

We write down the formula for finding the speed

v=S:t

Now let's write the solution of the problem in numbers:

v = 3: 3 = 1 km/min

How to find distance if time and speed are known?

To find the distance, if you know the time and speed, you need to multiply the time by the speed. An example of such a task:

The hare ran away from the Wolf at a speed of 1 kilometer in 1 minute. It took him three minutes to reach the hole. How far did the hare run?

Solution of the problem: We write in a draft what we know from the condition of the problem:

Hare speed - 1 kilometer in 1 minute

The time that the Hare ran to the hole - 3 minutes

Distance - unknown

Now, let's write the same with mathematical signs:

v - 1 km/min

t - 3 minutes

S-?

Remember the formula for finding distance:

S = v ⋅ t

Now let's write the solution of the problem in numbers:

S = 3 ⋅ 1 = 3 km

How to learn to solve challenging tasks?

To learn how to solve more complex problems, you need to understand how simple ones are solved, remember what signs indicate distance, speed and time. If you can't remember mathematical formulas they need to be written out on a piece of paper and always kept at hand while solving problems. Solve simple tasks with your child that you can think of on the go, for example, while walking.

A child who can solve problems can be proud of himself

When they solve problems about speed, time and distance, they often make a mistake because they forgot to convert units of measurement.

IMPORTANT: Units of measurement can be any, but if one task has different units measurements, translate them the same. For example, if the speed is measured in kilometers per minute, then the distance must be presented in kilometers, and the time in minutes.

For the curious: The now generally accepted system of measures is called metric, but it was not always so, and in the old days in Russia other units of measurement were used.

Boa problem: An elephant calf and a monkey measured the length of the boa constrictor with steps. They were moving towards each other. The speed of the monkey was 60 cm in one second, and the speed of the baby elephant was 20 cm in one second. They took 5 seconds to measure. What is the length of the boa constrictor? (solution below picture)

Solution:

From the condition of the problem, we determine that we know the speed of the monkey and the baby elephant and the time it took them to measure the length of the boa constrictor.

Let's write this data:

Monkey speed - 60 cm / sec

Elephant speed - 20 cm / sec

Time - 5 seconds

Distance unknown

Let's write this data in mathematical signs:

v1 - 60 cm/sec

v2 - 20 cm/sec

t - 5 seconds

S-?

Let's write the formula for the distance if the speed and time are known:

S = v ⋅ t

Let's calculate how far the monkey traveled:

S1 = 60 ⋅ 5 = 300 cm

Now let's calculate how much the baby elephant walked:

S2 = 20 ⋅ 5 = 100 cm

We sum up the distance that the monkey walked and the distance that the baby elephant walked:

S=S1+S2=300+100=400cm

Graph of body speed versus time: photo

The distance traveled at different speeds is covered in different times. The higher the speed, the less time it takes to move.

Table 4 class: speed, time, distance

The table below shows the data for which you need to come up with tasks, and then solve them.

№	Speed ​​(km/h)	Time (hour)	Distance (km)
1	5	2	?
2	12	?	12
3	60	4	?
4	?	3	300
5	220	?	440

You can dream up and come up with tasks for the table yourself. Below are our options for the task conditions:

1. Mom sent Little Red Riding Hood to Grandma. The girl was constantly distracted and walked through the forest slowly, at a speed of 5 km/h. She spent 2 hours on the way. How far did Little Red Riding Hood travel during this time?
2. The postman Pechkin carried a parcel on a bicycle at a speed of 12 km / h. He knows that the distance between his house and Uncle Fyodor's house is 12 km. Help Pechkin calculate how long it will take to travel?
3. Ksyusha's dad bought a car and decided to take his family to the sea. The car was traveling at a speed of 60 km / h and 4 hours were spent on the road. What is the distance between Ksyusha's house and the sea coast?
4. The ducks gathered in a wedge and flew to warmer climes. The birds flapped their wings tirelessly for 3 hours and overcame 300 km during this time. What was the speed of the birds?
5. An AN-2 plane flies at a speed of 220 km/h. He took off from Moscow and flies to Nizhny Novgorod, the distance between these two cities is 440 km. How long will the plane be on the way?

The answers to these questions can be found in the table below:

№	Speed ​​(km/h)	Time (hour)	Distance (km)
1	5	2	10
2	12	1	12
3	60	4	240
4	100	3	300
5	220	2	440

Examples of solving problems for speed, time, distance for grade 4

If there are several objects of movement in one task, you need to teach the child to consider the movement of these objects separately and only then together. An example of such a task:

Two friends Vadik and Tema decided to take a walk and left their houses towards each other. Vadik rode a bicycle, and Tema walked. Vadik was driving at a speed of 10 km/h, and Tema was walking at a speed of 5 km/h. They met an hour later. What is the distance between the houses of Vadik and Tema?

This problem can be solved using the formula for the dependence of distance on speed and time.

S = v ⋅ t

The distance that Vadik traveled on a bicycle will be equal to his speed multiplied by the travel time.

S = 10 ⋅ 1 = 10 kilometers

The distance that the Subject has traveled is considered similarly:

S = v ⋅ t

We substitute in the formula the digital values ​​\u200b\u200bof its speed and time

S = 5 ⋅ 1 = 5 kilometers

The distance that Vadik traveled must be added to the distance that Tema traveled.

10 + 5 = 15 kilometers

How to learn to solve complex problems that require logical thinking?

Develop logical thinking child, you need to solve with him simple, and then complex logical tasks. These tasks may consist of several stages. You can go from one stage to another only if the previous one is solved. An example of such a task:

Anton rode a bicycle at a speed of 12 km/h, and Liza rode a scooter at a speed 2 times less than Anton's, and Denis walked at a speed 2 times less than Lisa's. What is the speed of Denis?

To solve this problem, you must first find out the speed of Lisa and only after that the speed of Denis.

Who is driving faster? Question about friends

Sometimes in textbooks for grade 4 there are difficult tasks. An example of such a task:

Two cyclists left different cities towards each other. One of them was in a hurry and raced at a speed of 12 km / h, and the second was driving slowly at a speed of 8 km / h. The distance between the cities from which the cyclists left is 60 km. How far will each cyclist travel before they meet? (solution below photo)

Solution:

• 12+8 = 20 (km/h) is the combined speed of the two cyclists, or the speed at which they approached each other
• 60 : 20 = 3 (hours) is the time after which the cyclists met
• 3 ⋅ 8 = 24 (km) is the distance traveled by the first cyclist
• 12 ⋅ 3 = 36 (km) is the distance traveled by the second cyclist
• Check: 36+24=60 (km) is the distance traveled by two cyclists.
• Answer: 24 km, 36 km.

Invite children to solve such problems in the form of a game. Perhaps they themselves want to make up their own problem about friends, animals or birds.

VIDEO: Movement tasks