The average speed on two parts of the path. What formula is calculated by the average speed

In school, each of us came across the task like the following. If the car part of the path moved at one speed, and the next cut part on the other, how to find middle speed?

What is this value and why is it needed? Let's try to figure it out.

Speed \u200b\u200bin physics is the value describing the number of paths passed per unit of time. That is, when they say that the pedestrian speed is 5 km / h, which means that it passes the distance of 5 km in 1 hour.

The formula for finding speed looks like this:
V \u003d S / T, where S is the path traveled, T is time.

There is no single dimension in this formula, since it is also described and extremely slow, and very rapid processes.

For example, an artificial satellite of the Earth overcomes about 8 km in 1 second, and the tectonic plates on which the continents are located, on the measurements of scientists, diverge only a few millimeters per year. Therefore, the dimension at speed can be different - km / h, m / s, mm / s, etc.

The principle is that the distance is divided by the time required to overcome the path. Do not forget about dimension if complex calculations are carried out.

In order not to get confused and not mistaken in the answer, all the values \u200b\u200bare given in the same measurement units. If the length of the path is indicated in kilometers, and some part of it in centimeters, while we do not get unity in the dimension, we can not find out the right answer.

Permanent speed

Description of the formula.

The easiest case in physics is a uniform movement. The speed is constant, does not change throughout the path. There are even speed constants reduced to the tables - unchanged values. For example, the sound propagates in the air at a speed of 340.3 m / s.

And the light is an absolute champion in this regard, it has the biggest speed in our universe - 300,000 km / s. These values \u200b\u200bdo not change from the starting point of the movement to the final. They depend only on the medium in which they move (air, vacuum, water, etc.).

Uniform movement is often found to us in everyday life. So the conveyor is working at a factory or factory, a funicular on mountain ranges, an elevator (with the exception of very short periods of start-up and stop).

The schedule of such a movement is very simple and is a straight line. 1 second - 1 m, 2 seconds - 2 m, 100 seconds - 100 m. All points are on one straight line.

Uneven speed

Unfortunately, it is ideal in life, and in physics it is extremely rare. Many processes pass with uneven speed, then accelerating, slow down.

Let's imagine the movement of an ordinary long-distance bus. At the beginning of the way, he accelerates, the traffic lights slow down, and it stops at all. Then goes faster outside the city, but slowly slowly, and on the descents again accelerates.

If you depict this process in the form of a graph, you will get a very intricate line. Determine the speed according to the graphic can only for some particular point, and common principle not.

A whole set of formulas will be required, each of which is suitable only for its drawing site. But there is nothing terrible. To describe the movement of the bus use averaged value.

You can find the average speed of movement in the same formula. Indeed, we know the distance between bus stals, the time is measured on the way. Sharing one thing to another, find the desired value.

What is it for?

Such calculations are useful to everyone. We all plan on your day and move. Having a cottage behind the city, it makes sense to find out the average track speed when traveling there.

It will simplify the planning of the weekend. Having learned to find this magnitude, we can be more punctual, stop being late.

Let's go back for example, proposed at the very beginning, when part of the road car drove at one speed, and the other - with another. This type of task is very often used in school Program. Therefore, when your child will ask you to help him with a solution to such a question, you will just do it.

Folding the length of the paths, you will receive a total distance. Sharing their values \u200b\u200bto the speed specified in the source data, you can determine the time spent on each of the plots. Folding them, we get the time spent on the whole way.

Often the driver needs to find such an important indicator as the average vehicle speed after a particular trip. Sometimes this figure will be an important fact for the driver's transport driver, and in other cases - just an interesting number For the owner of the vehicle. In any case, the calculation of medium speed is important for many drivers. In modern cars equipped with efficient computer control systems, it is enough just to select the desired display mode on the computer screen to find out the average speed for a certain period of time or mileage.

To calculate the middle speed of the trip on modern car It is enough to prepare in advance by resetting the rate of daily mileage to zero, as well as resetting the average flow data and speed. After that, you can not block any time, and also not to think out the formula for calculating the average speed of the trip. Nevertheless, this option is not always suitable, and not all cars are equipped with a good on-board computer. Therefore, it should be sorted out how to determine the average speed and other parameters.

Find average speed and average ride consumption in fact

If the measurements of the middle speed of the trip are important for you for commercial purposes or as reporting for the company in which you work, it is easiest to buy a GPS navigator that has a function of accounting for speed and time spent on the road. This device will completely replace the on-board computer and will be able without the use of various formulas to show you the average travel speed.

In other cases, you can use more rude methods for definition. For measurements you will need a stopwatch that will determine working time Trips. That is, every second, which car spends on the road is important. The time spent at refueling or roadside cafes is often not included in the calculation. Tasks for accurate measurement are as follows:

before your trip, reset the daily kilometers counter to zero, start a new run report;
install the Stopwatch car on the dashboard and do not forget to turn it on every time when you touch;
as soon as you stopped not because of the road situation, but own willing, turn off the stopwatch;
after arriving at the destination, write out the daily meter data with an accuracy of one kilometer;
also, write down the data of the stopwatch with an accuracy of the minute - this will give you the opportunity to unleash the equation;
substitute the data obtained in the Vsher formula \u003d S / T, where V is the average speed, S is the distance traveled, and T - the time spent on the trip.

Suppose you left exactly 5 hours on the trip, and the distance passed on the speedometer turned out to be 300 kilometers. This means that the average speed of your car during the movement was 60 km / h. If you practice the definition of medium speed for each long trip, you will be surprised by low indicators.

It is often the impression that the average speed should be about 120 kilometers per hour, but in fact it turns out less than 60. Similarly, you can calculate the average fuel consumption. It is necessary to share the liters for hundreds of kilometers through the distance. For example, if you drove 300 kilometers, then you need to make a sum of lithra at 3.

What should be the average speed of the car on the trip?

Many are wondering, and what actually there should be an average vehicle speed. Squisted amazing fact The fact that the average speed of the car in the route was only 80 kilometers per hour, the driver begins to doubt that it effectively uses the resource of the vehicle. In fact, this speed is quite admissible.

The optimal speed when moving on the highway is 90 km / h, but it does not always get to keep the cruising speed constantly. Sometimes there are situations that are forced for a few minutes to go slowly. For example, you can reach the truck, waiting for the possibility of overtaking. The optimal average speed on the track will depend on such factors:

road conditions and condition of the road, on which the trip in the place you need is running;
the number of transport, the load and complexity of the track for completing the overtooks of slow cars;
the presence of additional strips for maneuver without reducing the speed of the machine;
the speed and availability of automatic fixation of traffic violations or traffic police posts;
personal security considerations that come from the state of their own car;
type of transport where you overcome the distance, its technical capabilities and restrictions;
weather conditions, the presence of ice crusts on the highway or wet road that reduces good grip.

It is only basic factorswhich affect the average speed of the machine at the track. In practice, in the absence of traffic violations, the average vehicle speed on the track is 75-80 kilometers per hour. Achieve an average speed of 90 km / h is possible only on a certain segment of the track. Therefore, do not be mistaken, seeing small values \u200b\u200bon the on-board computer screen.

The first factor to be assessed when choosing a high-speed mode on the track is safety. This one important criterion Sometimes it becomes a victim of a lack of time or desire to show decent digits of medium speed. In fact, such purposes never lead to good consequences, so always choose safe modes Trips.

Optimum speed for the car - the second trick mode selection factor

The main criterion for choosing the speed mode is far from the possibility of the machine, but your considerations about the safety and confidence of the trip. If you think that you have to drive at a speed of 90 km / h under these conditions it is dangerous, it is better to choose a more comfortable and confident mode. Nevertheless, there are certain recommendations from manufacturers.

The first thing you should remember in such a conversation conversation is the average consumption. If you support the speed of the machine at 90 kilometers per hour, then the flow rate will be as close as possible to the passport indicators of the flow rate on the track. Many drivers are worried about the fact that their car on the track consumes more fuel than specified in the documents. This happens for such reasons:

on overtaking, the car is forced to consume more fuel due to the need for rapid acceleration;
permanent braking and starting in traffic or on various obstacles also gives plus to consumption;
movement at speeds over 100 kilometers per hour begins to significantly increase gasoline consumption;
the manufacturer calculates the track modes of the trip to the middle speed of 90 kilometers per hour;
under this indicator Setting all functions and assemblies of the car, gear ratios and engine.

It is for these reasons that average flow rates often turn out to be an order of magnitude more passport measurements. When determining the flow in the track mode for technical characteristics Machines The manufacturer performs transport testing is not a track where the machine is driving with a constant one recommended speed. This is what allows you to achieve such entertaining fuel consumption figures.

Let's sum up

The average vehicle speed is an important indicator that can explain the increased consumption and time delay that you experience in a given trip. You need to be able to calculate the average speed and know the parameters of the operation of your transport to choose optimal modes Trips. Such knowledge will never interfere with you, and will also help you understand many of the subtleties of the operation of the car.

If you decide to take into account the features of your operation of transport, should be started from accounting for medium speed when moving, as well as average flow rates. If you can take into account these indicators constantly, you can also improve the average consumption, because in this case sports interest will be wound. Do you account for the average operation of your car?

The average speed is called the speed that is obtained if the whole way to divide for the time for which the object overcame this path. Middle Speed \u200b\u200bFormula:

V cf \u003d S / T.

S \u003d S1 + S2 + S3 \u003d V1 * T1 + V2 * T2 + V3 * T3
V cf \u003d S / T \u003d (V1 * T1 + V2 * T2 + V3 * T3) / (T1 + T2 + T3)

To not be confused with clock and minutes, we translate all minutes to hours: 15 min. \u003d 0.4 hour, 36 min. \u003d 0.6 hour. We substitute numeric values \u200b\u200binto the last formula:

V cf \u003d (20 * 0.4 + 0.5 * 6 + 0.6 * 15) / (0.4 + 0.5 + 0.6) \u003d (8 + 3 + 9) / (0.4 + 0.5 + 0.6) \u003d 20/15 \u003d 13.3 km / h

Answer: Average velocity V cf \u003d 13.3 km / h.

How to find the average speed with acceleration

If the speed at the beginning of the move differs from the speed at its end, such a movement is called accelerated. And far from always the body really moves faster and faster. If the movement slows down, they still say that it moves with acceleration, only acceleration will be negative.

In other words, if the car, touched from the spot, acted in a second to a speed of 10 m / s, then its acceleration A is 10 m per second per second a \u003d 10 m / s. If the car stopped at the next second, then its acceleration is also 10 m / s², only already with a minus sign: a \u003d -10 m / s.

The speed of movement with acceleration at the end of the time segment is calculated by the formula:

V \u003d V0 ± AT,

where V0 is the initial speed of movement, A - acceleration, t - the time for which this acceleration was observed. Plus or minus in the formula is made depending on whether the speed has increased or decreased.

The average speed for the length of time T is calculated as the arithmetic average initial and final speed:

V cf \u003d (V0 + V) / 2.

Find average speed: task

The ball was pushed over a flat plane with the initial velocity V0 \u003d 5 m / s. After 5 seconds. The ball stopped. What is the acceleration and average speed?

The final speed of the ball V \u003d 0 m / s. Acceleration from the first formula is

a \u003d (V - V0) / T \u003d (0 - 5) / 5 \u003d - 1 m / s².

The average speed V cf \u003d (V0 + V) / 2 \u003d 5/2 \u003d 2.5 m / s.

2 . The first portion of 120 m long skier was held in 2 minutes, and he passed the second length of 27 m in 1.5 minutes. Find the average skier movement all over the way.

3 . Moving along the highway, the cyclist drove 20 km over 40 minutes, then he overcame for 2 min long, and the remaining 39 km 400 m along the highway he drove in 78 minutes. What is the average speed on the whole path?

4 . The boy for 25 minutes was 1.2 km away, then half an hour rested, and then ran another 800 m in 5 minutes. What was his average speed all over the way?

Level B.

1 . What speed is medium or instantaneous - this is speech In the following cases:

a) the bullet flies out of the rifle at a speed of 800 m / s;

b) the speed of the earth around the sun 30 km / s;

c) The maximum speed limiter is installed on the road - 60 km / h;

d) past you drove a car at a speed of 72 km / h;

e) The bus overcame the distance between Mogilev and Minsk at a speed of 50 km / h?

2 . The path of 63 km from one station to another electric train takes place in 1 h 10 min at an average speed of 70 km / h. What time does stop stopping?

3 . Self-propelled mower has a width of the capture of 10 m. Determine the area of \u200b\u200bthe field, bevelled in 10 minutes, if the average mower rate is 0.1 m / s.

4 . On the horizontal section of the path of the car drifted at a speed of 72 km / h for 10 minutes, and then drove a rise at a speed of 36 km / h per 20 min. What is the average speed on the whole path?

5 . Cyclist The first half of time when moving from one point to another was driving at a speed of 12 km / h, and the second half of the time (due to the prolque of the tire) was walking at a speed of 4 km / h. Determine the average cyclist speed.

6 . The schoolboy drove 1/3 of the total time by bus at a speed of 60 km / h, another 1/3 of the total time on a bike at a speed of 20 km / h, the rest of the time passed at a speed of 7 km / h. Determine the average speed of the schoolboy.

7 . The cyclist was driving from one city to another. Half the path he drove at a speed of 12 km / h, and the second half (due to the prolque of the bus) was walking at a speed of 4 km / h. Determine the average speed of its movement.

8 . From one point to another motorcyclist moved at a speed of 60 km / h, the return route was passed at a speed of 10 m / s. Determine the average speed of the motorcyclist for all the time of movement.

9 . The schoolboy drove 1/3 ways by bus at a speed of 40 km / h, another 1/3 ways to bike at a speed of 20 km / h, the last third of the way was held at a speed of 10 km / h. Determine the average speed of the schoolboy.

10 . Pedestrian part of the path was held at a speed of 3 km / h, spending 2/3 of his movement time. The remaining time he passed at a speed of 6 km / h. Determine the average speed.

11 . Train speed on the rise of 30 km / h, and on the descent - 90 km / h. Determine the average speed on the field of the path, if the descent is twice as long as lifting.

12 . Half of time when moving from one point to another car moved at a constant speed of 60 km / h. At what constant speed, it should move the remaining time if the average speed is 65 km / h?

Objectives for middle speed (hereinafter referred to as IC). We have already considered the tasks for a straight movement. I recommend to view the articles "" and "". Typical tasks for mid-speed is a group of movement tasks, they are included in the exam in mathematics and such a task may probably be in front of you at the time of the exam. Takers are simple, solved quickly.

The meaning is as follows: imagine the object of movement, such as a car. It passes certain areas of the path at different speeds. For all the way spent some time. So: the average speed is such a constant speed with which the car would overcome this news the path during the same time, that is, the mid-speed formula is as follows:

If the paths of the path were two, then

If three, then respectively:

* In the denominator, we summarize the time, and in the distance numerator covered for the corresponding periods of time.

The first third of the tracks of the car drove at a speed of 90 km / h, the second third - at a speed of 60 km / h, and the last one at a speed of 45 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

As already mentioned, it is necessary to split all the way for all the movement. The condition said about three parts of the path. Formula:

We denote all let S. Then the first third of the road the car was driving:

The second third of the road the car was driving:

The last third of the road car was driving:

In this way

Solve yourself:

The first third of the tracks of the car drove at a speed of 60 km / h, the second third - at a speed of 120 km / h, and the last - at a speed of 110 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

The first hour of the car was driving at a speed of 100 km / h, the following two hours - at a speed of 90 km / h, and then two hours - at a speed of 80 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

The condition said about three parts of the path. UK will search by the formula:

We are not given the paths of the path, but we can easily calculate them:

The first portion of the path was 1 ∙ 100 \u003d 100 kilometers.

The second portion of the path was 2 ∙ 90 \u003d 180 kilometers.

The third portion of the path was 2 ∙ 80 \u003d 160 kilometers.

Calculate speed:

Solve yourself:

The first two hours the car was driving at a speed of 50 km / h, the next hour - at a speed of 100 km / h, and then two hours - at a speed of 75 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

The first 120 km car was driving at a speed of 60 km / h, the next 120 km - at a speed of 80 km / h, and then 150 km - at a speed of 100 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

It is said about three sections of the path. Formula:

The length of the plots is given. We define the time that the car spent on each site: the first spent 120/60 hours, on the second section of 120/80 hours, on the third 150/100 hours. Calculate speed:

Solve yourself:

The first 190 km of the car drove at a speed of 50 km / h, the next 180 km - at a speed of 90 km / h, and then 170 km - at a speed of 100 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

Half of the time spent on the road, the car was driving at a speed of 74 km / h, and the second half of time - at a speed of 66 km / h. Find the SC of the car throughout the path. Give the answer in km / h.

* There is a task about the traveler who drives the sea. With the decision of the guys there are problems. If you do not see it, then go to the site! The registration button (input) is located in the main menu of the site. After registration, log in and update this page.

Traveler swam the sea on the yacht with average speed 17 km / h Back he flew on a sports plane at a speed of 323 km / h. Find the average traveler speed throughout the path. Give the answer in km / h.

Sincerely, Alexander.

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