All tasks in which there is movement of objects, their movement or rotation, are somehow connected with speed.
This term characterizes the movement of an object in space over a certain period of time - the number of units of distance per unit of time. He is a frequent "guest" of both sections of mathematics and physics. The original body can change its location both uniformly and with acceleration. In the first case, the speed is static and does not change during the movement, in the second, on the contrary, it increases or decreases.
How to find speed - uniform motion
If the speed of the body remained unchanged from the beginning of the movement to the end of the path, then we are talking about moving with constant acceleration - uniform movement. It can be straight or curved. In the first case, the trajectory of the body is a straight line.
Then V=S/t, where:
- V is the desired speed,
- S - distance traveled (total path),
- t is the total time of movement.
How to find speed - acceleration is constant
If an object was moving with acceleration, then its speed changed as it moved. In this case, the expression will help to find the desired value:
V \u003d V (beginning) + at, where:
- V (beginning) - the initial speed of the object,
- a is the acceleration of the body,
- t is the total travel time.
How to find speed - uneven motion
In this case, there is a situation when the body passes different parts of the path in different times.
S(1) - for t(1),
S(2) - for t(2), etc.
On the first section, the movement took place at a “tempo” V(1), on the second - V(2), and so on.
To find out the speed of an object moving all the way (its average value), use the expression:
How to find speed - rotation of an object
In the case of rotation, we are talking about the angular velocity, which determines the angle through which the element rotates per unit of time. The desired value is denoted by the symbol ω (rad / s).
- ω = Δφ/Δt, where:
Δφ – passed angle (angle increment),
Δt - elapsed time (movement time - time increment).
- If the rotation is uniform, the desired value (ω) is associated with such a concept as the period of rotation - how long will it take for our object to make 1 complete revolution. In this case:
ω = 2π/T, where:
π is a constant ≈3.14,
T is the period.
Or ω = 2πn, where:
π is a constant ≈3.14,
n is the frequency of circulation.
- With the known linear speed of the object for each point on the path of motion and the radius of the circle along which it moves, the following expression is required to find the speed ω:
ω = V/R, where:
V is the numerical value of the vector quantity (linear velocity),
R is the radius of the body's trajectory.
How to find speed - approaching and moving away points
In such tasks, it would be appropriate to use the terms approach speed and distance speed.
If the objects are heading towards each other, then the speed of approach (retreat) will be as follows:
V (approach) = V(1) + V(2), where V(1) and V(2) are the velocities of the corresponding objects.
If one of the bodies catches up with the other, then V (closer) = V(1) - V(2), V(1) is greater than V(2).
How to find speed - movement on a body of water
If events unfold on the water, then the speed of the current (i.e., the movement of water relative to a fixed shore) is added to the object’s own speed (movement of the body relative to the water). How are these concepts related?
In the case of moving downstream, V=V(own) + V(tech).
If against the current - V \u003d V (own) - V (flow).
Let's turn a school physics lesson into an 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 person walks fast, the other takes his time. 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, there is a direct road from home to a music school. 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? In technical terms, 30 minutes = 0.5 h = (1/2) h. If we solve the problem, it turns out that we 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 very 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.
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. For a 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 covered in different times and at different speeds.
How does travel time depend on speed?
The higher the 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?
- Read the problem carefully and determine what is known from the condition of the problem.
- Write this information on a draft.
- Also write what is unknown and what needs to be found
- Use the formula for problems about distance, time and speed
- 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:
- We write down in the draft that we know the distance and time.
- From the condition of the problem, we determine that we need to find the speed
- 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 more complex problems?
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, you need to write them out on a piece of paper and always keep them 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 there are different units of measurement 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 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)
Decision:
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:
- 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?
- 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?
- 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?
- 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?
- 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?
To develop the logical thinking of the child, you need to solve simple and then complex logical problems with him. 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 under photo)
Decision:
- 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
To find the speed, time and distance, you need to take a school textbook and read)) I liked such puzzles.
Speed is measured by the distance traveled in a certain time, so we divide the distance by the time and get, for example, kilometers per hour. Well, the rest of the quantities can be calculated based on this formula.
This question is about junior high school math.
Distance can be found by multiplying by each other the speed and time spent to overcome this distance.
So time is equal to distance divided by speed.
- In order to find out the speed, we divide the distance by the time;
- In order to find out the time, we divide the distance by the speed;
- To find the distance, multiply the speed by the time.
Everything is quite simple and easy, because everyone in school knew this formula - you just need to remember!)
Some people remember faster when they read and look, so looking at these formulas proposed in the image, you can remember them for almost a lifetime.
All three formulas are interconnected and one follows the other.
Movement tasks are one of the important topics for students. To solve problems, you need to know the rules for finding quantities. To find distance, multiply speed by time; to find time, divide distance by speed. To find the speed, you need to divide the distance by the time.
If the body moves uniformly, i.e. at a constant rate, it is very easy to determine one of these quantities if the other two are known.
Speed, distance and time are denoted by the letters V, S, t, respectively.
Speed: V=S/t
Distance: S=V*t
Time: t=S/V
To find the distance you need to multiply the speed by the travel time.
Divide distance by time to find speed.
To find the travel time, divide the distance by the speed.
Well, here's a picture of everything, here there are formulas with all designations.
To find physical quantities such as speed (V), time (t) and distance (S), you need to know that these quantities depend on movement.
The movement is uniformly accelerated, equally slowed down, uniform.
With uniformly accelerated and equally slow, the speed of envy depends on time. And with uniform - the speed does not change, i.e. constant.
The formulas are shown below:
Speed, time, distance - all these are physical quantities that are somehow connected with movement. The movement is either uniform or uniformly accelerated (and also uniformly slowed down). While in uniform motion the body moves with constant speedquot ;, which does not depend on time - uniformly accelerated speed can change over time.
How to find one of the three speed values, if we know the other two?
Well, to find out the time you need to divide the distance by the speed, of course the values of distance and speed must be known. To find out the speed, you need to divide the distance by the time, for example, you get a common value - mph.
The concept of time (as well as distance and speed) is a physical quantity. It characterizes the interval during which an object changes its properties and is used in physics and mathematics to solve motion problems.
As an example, let's try to find time if distance and speed are known, and also consider inverse methods for calculating unknown quantities.
Quick article navigation
Determine the time
To determine the time, a common formula is usually used: t \u003d S / v, where t is time, S is distance, and v is speed.
Thus, with the help of simple mathematical operations, one can calculate any of these quantities, knowing the other two. In this case, we have speed and distance values. To find time, we divide distance by speed.
The same formula will help calculate the speed, provided that the distance and time are known. To do this, we perform the simplest mathematical operations with ordinary fractions.
Determine the speed
From the formula by which we calculated the time, we calculate the speed. This is a value equal to the distance traveled per unit of time.
To find the speed value, you need to put it on one side of the equals sign, and other values on the other. To calculate the denominator in this equation, you need to divide the numerator by the value on the other side of the equal sign. That is, the distance is divided by the time and the following formula is obtained: v=S/t
Determine the distance
By analogy, we calculate the distance. It will be determined by the product of time and speed: S=v*t
