Velocity is how fast a point or body is moving. This is a vector quantity, and in order to set the speed, you must first set the speed value, as well as directly the direction in which it is measured. Consider how to calculate speed.
Usually, the speed is considered along the trajectory of the body. Then, the value will be defined as the path that was traveled per unit of time. In other words, to find the speed of a body, the path must be divided by the time it took to travel. And in this case, the formula for the speed of movement will look like this: V=S/t.
How to calculate average speed?
In kinematics, this concept is nothing more than an average characteristic of the speed of particles during their movement. There are two main ways to calculate average speed. The average speed of the path is the speed at which the length of the path traveled by the body is related to the time it took to travel. Such speed, unlike instantaneous speed, is not a vector quantity. If the body moved at the same speeds for equal periods of time, the average speed will be equal to the arithmetic mean of the speeds. But, if half of the path was at the same speed, and the second half at the other, the average speed will be equal to the harmonic mean of all the speeds taken separately, which will be equal to each other on different sections of the road. The calculation formula is as follows:
How to calculate average speed over displacement?
The average speed can also be derived from the displacement, it will be vectorial, that is, equal in relation to the time for which it was made. In this case, the average speed will be equal to zero if the body actually moved. If the movement took place in a straight line, then the average ground speed will be equal to the modulus of the average speed for the movement. The formula looks like this:
How to calculate stopping speed?
The braking distance is the distance that the vehicle travels from the moment it affects the braking system of the vehicle until it comes to a complete stop. The length of the braking distance depends on both the mass and the speed, as well as the condition of the roadway, weather conditions, tires, and so on. In addition, it also depends on the technological features of the vehicle. Depending on the type of brake pads the vehicle has, the logic of the electronic devices, and other parameters, the braking distance will be different. The braking distance initially depends on the energy of the body, which must be extinguished. This energy is determined by the following formula: E= m*V^2/2. It follows from it that if the same effort is given to braking, then the braking distance will be directly proportional to the mass of the body and square to the speed.
Units of measurement, of course, are very important for all kinds of calculations, as for the calculation of the speed of movement, then the units of measurement will be the units of measurement of speed. But, it is important not only to know them, you need to be able to translate values into different values. For example, speed is measured in meters per second (m/s), how to convert such a value, for example, to kilometers per second? Everything is simple! One meter per second contains six thousand centimeters per minute and, accordingly, one hundred centimeters per second. Also, one meter per second is three thousand six hundred meters per hour and sixty meters per minute. And three and six kilometers per hour is one meter per second. We hope that now those who read this article will not have questions about how to calculate the speed of movement.
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
For all stages of the gearbox and additional box, the values of the vehicle speed are calculated depending on the engine crankshaft speed (in agreement with the manager, the calculation can only be made for the highest stage of the additional box).
The calculation is carried out according to the formula
where v - vehicle speed, km/h;
n - frequency of rotation of the crankshaft of the engine, rpm;
rTo - rolling radius, m;
and 0 - gear ratio of the main gear;
andto - gear ratio of the calculated gear stage;
andd - gear ratio of the calculated stage of the additional (transfer) box.
The values of the crankshaft speed are taken the same as in the construction of the external speed characteristic.
Calculated values vt are entered in column 4 of the table. 2.1. Graphs of the dependence of the speed of the car on the frequency of rotation of the crankshaft of the engine are a series of rays coming out at different angles from the origin of coordinates, Figure 2.2.
Rice. 2.2 Dependences of the speed of the car on the frequency of rotation of the crankshaft in gears.
2.6. Traction characteristics and traction balance of the vehicle
The traction characteristic is the dependence of the vehicle's traction force on the speed of movement in gears. Traction values RT are calculated at individual points by the formula
where MTo - engine torque, Nm;
η T - transmission efficiency.
Calculation results RT are entered in column 7 of the table. 2.1, and dependency graphs are built on them RT = f(V) by transfers.
The traction balance of a vehicle is described by the traction or force balance equation
RT = Rd+ Rin+ Rand, (2.27)
where RT - traction force of the car, N;
Rd - total resistance force of the road, N;
Rin - air resistance force, N;
Rand - the force of inertia of the car, N.
Value Rd is determined by the expression
Rd = Gaψ , (2.28)
where Ga - gross vehicle weight, N; ψ - total road resistance coefficient.
The total drag coefficient of the road is a value that depends on the speed of the vehicle. However, taking into account this dependence greatly complicates the performance of the traction calculation and at the same time does not provide a clarification important for practice. Therefore, when performing a traction calculation, it is recommended to take the value ψ constant, equal to the value that was calculated for the maximum vehicle speed when determining the engine power required to drive at maximum speed, i.e. take everywhere ψ=ψ v.
For any one chosen value ψ magnitude Rd remains constant for all calculated points in all gears. Therefore, the value Rd counted once and not entered in the table. On the graph of the traction characteristic, the dependence PT= f(v) represented as a straight line parallel to the x-axis.
Rice. 2.3 Traction characteristics of the car.
Air drag force Rin amounts to
where withX - coefficient of longitudinal aerodynamic force;
Rin - air density, kg/m3;
toin - streamlining coefficient, kg/m 3 ;
F - frontal area of the car, m;
vin - air flow speed relative to the vehicle, km/h.
When calculating, you can set ρ in=1.225 kg/m. The airflow speed is usually assumed to be equal to the vehicle speed.
Values Rin calculated for all points and entered in column 5 of the table. 2.1. dependency graph Rin on velocity is a parabola passing through the origin.
For the convenience of further analysis, this graph is shifted upwards by an amount equal toR d (on the scale accepted for forces). In fact, with such a construction, this graph expresses the dependence( P in + P d )= f ( v ).
Vehicle inertia Rand after calculation Rd and Rin can be defined as the closing term of the force balance
(2.30)
On the graph, the valueR and is determined by a segment of a straight line drawn for the desired speed value parallel to the y-axis, between the points of intersection of this straight line of the graphs P T = f [ v ) and( P d + P in )= f ( v ). If a given speed can be achieved in several gears, then each of these gears will have its own value of the inertia force. Calculated values R and should be entered in column 6 of the table. 2.1.
The value of P T is entered in column 7 of the table. 2.1. The traction characteristic of the car is shown in fig. 2.3.
This article is about how to find the average speed. The definition of this concept is given, and two important particular cases of finding the average speed are considered. A detailed analysis of tasks for finding the average speed of a body from a tutor in mathematics and physics is presented.
Determination of average speed
medium speed the movement of the body is called the ratio of the path traveled by the body to the time during which the body moved:
Let's learn how to find it on the example of the following problem:
Please note that in this case this value did not coincide with the arithmetic mean of the speeds and , which is equal to:
m/s.
Special cases of finding the average speed
1. Two identical sections of the path. Let the body move the first half of the way with the speed , and the second half of the way — with the speed . It is required to find the average speed of the body.
2. Two identical movement intervals. Let the body move at a speed for a certain period of time, and then began to move at a speed for the same period of time. It is required to find the average speed of the body.
Here we got the only case when the average speed of movement coincided with the arithmetic average speeds and on two sections of the path.
Finally, let's solve the problem from the All-Russian Olympiad for schoolchildren in physics, which took place last year, which is related to the topic of our today's lesson.
| The body moved with, and the average speed of movement was 4 m/s. It is known that for the last few seconds the average velocity of the same body was 10 m/s. Determine the average speed of the body for the first s of movement. |
The distance traveled by the body is: 
m. You can also find the path that the body has traveled for the last since its movement: m. Then for the first since its movement, the body has overcome the path in m. Therefore, the average speed on this section of the path was: 
m/s.
They like to offer tasks for finding the average speed of movement at the Unified State Examination and the OGE in physics, entrance exams, and olympiads. Every student should learn how to solve these problems if he plans to continue his education at the university. A knowledgeable friend, a school teacher or a tutor in mathematics and physics can help to cope with this task. Good luck with your physics studies!
Sergey Valerievich
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.