The formula for the dependence of time, speed and distance: Grade 4. How to find time, knowing speed and distance? How to find speed if time and distance is known? How to find a distance if time and speed is known? Graph of body velocity on time: photo

How to solve movements for movement? The formula of dependence between speed, time and distance. Tasks and solutions.

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

People, animals or cars can move at a certain speed. For a certain time, they can go a certain path. For example: today you can reach your school in half an hour. You go at a certain speed and overcome 1000 meters in 30 minutes. The path that is overcome is designated in mathematics by the letter S.. The speed is indicated by the letter v. And the time for which the path has been denied is indicated by the letter t. 

• Way - S.  
• Speed \u200b\u200b- v
• Time - t 

If you are late to school, you can go the same way in 20 minutes, increasing your speed. So, the same path can be traveled over different times and at different speeds.

How does the passage time dependent on speed?

The larger the speed, the faster the distance will be made. And the lower the speed, the more time you need to pass the path.

How to find time, knowing speed and distance?

In order to find the time you need to pass the path, you need to know the distance and speed. If the distance is divided into speed, you will find out the time. An example of such a task:

The task of the hare. The hare ran away from the wolf at a speed of 1 kilometer per minute. He ran to his hole 3 kilometers. For what time did the hare reach a hole?

How is it easy to solve the problems for movement, where you need to find a distance, time or speed?

1. Carefully read the task and determine what is known from the conditions of the problem.
2. Write this data on the draft.
3. Also write what is unknown and what needs to be found
4. Use the formula for tasks about distance, time and speed
5. Enter the known data in the formula and solve the problem

Solution for the problem about the hare and the wolf.

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

We write to the draft these data for example:

Distance to hole - 3 kilometers

Hare speed - 1 kilometer in 1 minute

Time is unknown

Now we write the same as mathematical signs:

S. - 3 kilometers

V - 1 km/min

  t — ?

We recall and write a formula to find the time in the notebook:

  t \u003d s: v

Now we write down the solution of the problem with numbers:

  t \u003d 3: 1 \u003d 3 minutes

 How to find speed if time and distance is known?

In order to find speed, if time and distance are known, the distance must be divided for a while. An example of such a task:

The hare ran away from the wolf and ran to his hole 3 kilometers. He overcame this distance in 3 minutes. At what speed did the hare run?

Solving the problem of movement:

1. In the draft, we write down that we know the distance and time.
2. From the conditions of the problem, we determine what needs to be found speed
3. Remember the formula for finding speed.

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

We substitute the known data and solve the problem:

Distance to hole - 3 kilometers

The time for which the hare reached the hole is 3 minutes

Speed \u200b\u200bis unknown

We write these known data with mathematical signs

S. - 3 kilometers

  t - 3 minutes

v -?

Record the formula to find speed

v \u003d s: t

Now we write down the solution of the problem with numbers:

v \u003d 3: 3 \u003d 1 km/min

How to find a distance if time and speed is known?

To find a distance, if it is known time and speed, it is necessary to multiply by 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 run to the hole. What distance did the hare run?

Solution of the problem: We write to a draft that we know from the conditions of the problem:

Hare speed - 1 kilometer in 1 minute

The time that the hare fled to Nora is 3 minutes

Distance is unknown

Now, we will write the same thing with mathematical signs:

v - 1 km/min

  t - 3 minutes

S -?

Remember the formula for finding the distance:

S \u003d V ⋅ T

Now we write down the solution of the problem with numbers:

S \u003d 3 ⋅ 1 \u003d 3 km

How to learn to solve more complex problems?

To learn how to solve more complex tasks, you need to understand how simple tasks are solved, remember which signs indicate the distance, speed and time. If it is not possible to remember the mathematical formulas, they need to be written out on a sheet of paper and always keep at hand while solving problems. Solve with your child simple tasks that can be invented on the go, for example, during a walk.

Units

When they solve problems about speed, time and distance, they often make a mistake, due to the fact that they forgot to translate units of measurement.

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

For curious: The generally accepted system of measures is called metric now, but this was not always the case, and in the old days in Rus' other units of dimension were used.

The task of the boas: The elephant and the monkey measured the length of the boa constrictor with steps. They moved towards each other. The speed of the monkey was 60 cm in one second, and the elephant speed is 20 cm in one second. They spent 5 seconds on measurement. What is the length of the boa constrictor? (decision under the picture)

Decision:

From the conditions of the problem, we determine that we know the speed of the monkey and the elephant and the time that they needed to measure the length of the boost.

We write down these data:

Monkey speed - 60 cm/s

Elephant speed - 20 cm/s

Time - 5 seconds

The distance is unknown

We write this data with mathematical signs:

v1 - 60 cm/s

v2 - 20 cm/s

t - 5 seconds

S -?

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

S \u003d V ⋅ T

We calculate how distance the monkey has passed:

S1 \u003d 60 ⋅ 5 \u003d 300 cm

Now let's calculate how much the elephant has passed:

S2 \u003d 20 ⋅ 5 \u003d 100 cm

We summarize the distance that the monkey and the distance that the elephant passed:

S \u003d S1 + S2 \u003d 300 + 100 \u003d 400 cm

Graph of body velocity on time: photo

The distance overcome with different speeds is overcome in different times. The larger the speed, the less time it will take.

Table 4 class: speed, time, distance

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

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

1. Mom sent a red hat to her grandmother. The girl was constantly distracted and walked through the forest slowly, at a speed of 5 km/h. She spent 2 hours on the path. What distance has a red cap passed during this time?
2. The postman Pechkin takes a parcel on a bicycle at a speed of 12 km/h. He knows that the distance between his house and the house of Uncle Fedor is 12 km. Help Pechkin calculate how long will it take for the road?
3. Dad Ksyusha bought a car and decided to take his family to the sea. The car was driving at a speed of 60 km/h and 4 hours were spent on the road. What is the distance between the house of Ksyusha and the sea coast?
4. The ducks gathered in the wedge and flew into the warm edges. The birds waved their wings tired for 3 hours and overcame 300 km during this time. What was the speed of birds?
5. The An-2 aircraft flies at a speed of 220 km/h. He flew out of Moscow and flies to Nizhny Novgorod, the distance between these two cities is 440 km. How long will the plane go along?

The answers to the above tasks can be found in the table below:

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 of Vadik and the topic decided to take a walk and left their houses towards each other. Vadik rode a bicycle, and the topic was walking. Vadik rode at a speed of 10 km/h, and the topic was at a speed of 5 km per hour. An hour later they met. What is the distance between Vadik's houses and topics?

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

S \u003d V ⋅ T

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

S \u003d 10 ⋅ 1 \u003d 10 kilometers

The distance that the topic has passed is considered similarly:

S \u003d V ⋅ T

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

S \u003d 5 ⋅ 1 \u003d 5 kilometers

The distance that Vadik drove must be added to the distance that the topic passed.

10 + 5 \u003d 15 kilometers

How to learn how to solve complex problems, for solving which you need to think logically?

To develop the logical thinking of the child, you need to solve with him simple, and then complex logical problems. These tasks may consist of several stages. It is only possible to move from one stage to another if the previous one is resolved. An example of such a task:

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

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

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

Two cyclists left different cities towards each other. One of them hurried and raced at a speed of 12 km/h, and the second rode slowly at a speed of 8 km/h. The distance between the cities from which cyclists left 60 km. What distance will each cyclist pass, before they meet? (decision under the photo)

Decision:

• 12+8 \u003d 20 (km/h) is the total speed of two cyclists, or the speed with which they approached each other
• 60 : 20 \u003d 3 (hours) - this is the time through which cyclists met
• 3 ⋅ 8 \u003d 24 (km) is the distance that the first cyclist drove
• 12 ⋅ 3\u003d 36 (km) is the distance that the second cyclist drove
• Check: 36+24 \u003d 60 (km) is the distance that two cyclists traveled.
• Answer: 24 km, 36 km.

Offer children in the form of a game to solve such problems. Perhaps they themselves will want to compose their task about friends, animals or birds.

Video: Movement tasks