How to find the average speed in physics 9. How to find the average speed of a car after driving in different modes

Medium speed tasks (hereinafter referred to as SV). We have already looked at tasks involving linear motion. I recommend looking at the articles "" and "". Typical tasks for average speed are a group of movement problems, they are included in the Unified State Examination in mathematics, and such a task may very likely appear in front of you at the time of the exam itself. The problems are simple and can be solved quickly.

The idea is this: imagine an object of movement, such as a car. He travels certain sections of the path at different speeds. The entire journey takes a certain amount of time. So: average speed is such a constant speed with which a car would cover a given distance in the same time. That is, the formula for average speed is as follows:

If there were two sections of the path, then

If three, then accordingly:

*In the denominator we sum up the time, and in the numerator the distances traveled during the corresponding time intervals.

The car drove the first third of the route at a speed of 90 km/h, the second third at a speed of 60 km/h, and the last third at a speed of 45 km/h. Find the car's IC along the entire route. Give your answer in km/h.

As already said, it is necessary to divide the entire path into the entire time of movement. The condition says about three sections of the path. Formula:

Let us denote the whole by S. Then the car drove the first third of the way:

The car drove the second third of the way:

The car drove the last third of the way:

Thus

Decide for yourself:

The car drove the first third of the route at a speed of 60 km/h, the second third at a speed of 120 km/h, and the last third at a speed of 110 km/h. Find the car's IC along the entire route. Give your answer in km/h.

The car drove for the first hour at a speed of 100 km/h, for the next two hours at a speed of 90 km/h, and then for two hours at a speed of 80 km/h. Find the car's IC along the entire route. Give your answer in km/h.

The condition says about three sections of the path. We will search for the SC using the formula:

The sections of the path are not given to us, but we can easily calculate them:

The first section of the route was 1∙100 = 100 kilometers.

The second section of the route was 2∙90 = 180 kilometers.

The third section of the route was 2∙80 = 160 kilometers.

We calculate the speed:

Decide for yourself:

The car drove at a speed of 50 km/h for the first two hours, at a speed of 100 km/h for the next hour, and at a speed of 75 km/h for two hours. Find the car's IC along the entire route. Give your answer in km/h.

The car drove for the first 120 km at a speed of 60 km/h, for the next 120 km at a speed of 80 km/h, and then for 150 km at a speed of 100 km/h. Find the car's IC along the entire route. Give your answer in km/h.

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

The length of the sections is given. Let's determine the time that the car spent on each section: 120/60 hours were spent on the first section, 120/80 hours on the second section, 150/100 hours on the third. We calculate the speed:

Decide for yourself:

The car drove for the first 190 km at a speed of 50 km/h, for the next 180 km at a speed of 90 km/h, and then for 170 km at a speed of 100 km/h. Find the car's IC along the entire route. Give your answer in km/h.

Half the time spent on the road, the car was traveling at a speed of 74 km/h, and the second half of the time at a speed of 66 km/h. Find the vehicle's IC along the entire route. Give your answer in km/h.

*There is a problem about a traveler who crossed the sea. The guys have problems with the solution. If you don't see it, then register on the site! The registration (login) button is located in the MAIN MENU of the site. After registration, log in to the site and refresh this page.

The traveler crossed the sea on a yacht with average speed 17 km/h. He flew back on a sports plane at a speed of 323 km/h. Find the traveler's average speed along the entire journey. Give your answer in km/h.

Sincerely, Alexander.

P.S: I would be grateful if you tell me about the site on social networks.

There are average values, the incorrect definition of which has become a joke or a parable. Any incorrect calculations are commented on with a common, generally understood reference to such an obviously absurd result. For example, the phrase “average temperature in the hospital” will make everyone smile with sarcastic understanding. However, the same experts often, without thinking, add up the speeds on individual sections of the route and divide the calculated sum by the number of these sections in order to get an equally meaningless answer. Let us recall from the high school mechanics course how to find the average speed in the correct, not absurd, way.

Analogue of "average temperature" in mechanics

In what cases do the tricky conditions of a problem push us to a hasty, thoughtless answer? If they talk about “parts” of the path, but do not indicate their length, this alarms even a person who is little experienced in solving such examples. But if the problem directly indicates equal intervals, for example, “for the first half of the path the train followed at a speed...”, or “the pedestrian walked the first third of the path at a speed...”, and then describes in detail how the object moved at the remaining equal intervals. areas, that is, the ratio is known S 1 = S 2 = ... = S n and exact speed values v 1, v 2, ... v n, our thinking often misfires unforgivably. The arithmetic mean of the speeds is considered, that is, all known values v add up and divide into n. As a result, the answer turns out to be incorrect.

Simple “formulas” for calculating quantities during uniform motion

Both for the entire distance traveled and for its individual sections in the case of averaging the speed, the relations written for uniform motion are valid:

• S = vt(1), "formula" path;
• t=S/v(2), "formula" for calculating movement time ;
• v=S/t(3), “formula” for determining the average speed on a section of track S traversed in time t.

That is, to find the desired value v using relation (3), we need to know the other two exactly. It is when solving the question of how to find the average speed of movement that we first of all must determine what the entire distance traveled is S and what is the entire movement time? t.

Mathematical Hidden Error Detection

In the example we are solving, the distance traveled by the body (train or pedestrian) will be equal to the product nS n(since we n once we add up equal sections of the path, in the given examples - halves, n=2, or thirds, n=3). We know nothing about the total time of movement. How to determine the average speed if the denominator of the fraction (3) is not explicitly specified? Let us use relation (2), for each section of the path we determine t n = S n: v n. Amount We will write the time intervals calculated in this way under the line of the fraction (3). It is clear that in order to get rid of the "+" signs, you need to bring everything S n: v n to a common denominator. The result is a “two-story fraction.” Next, we use the rule: the denominator of the denominator goes into the numerator. As a result, for the train problem after reduction by S n we have v av = nv 1 v 2: v 1 + v 2, n = 2 (4) . For the case of a pedestrian, the question of how to find the average speed is even more difficult to solve: v av = nv 1 v 2 v 3: v 1v2 + v 2 v 3 + v 3 v 1,n=3(5).

Explicit confirmation of the error "in numbers"

In order to confirm with one’s fingers that determining the arithmetic mean is the wrong way to do calculations vWed, let’s make the example more concrete by replacing abstract letters with numbers. For the train, let's take the speeds 40 km/h And 60 km/h(wrong answer - 50 km/h). For a pedestrian - 5 , 6 And 4 km/h(average - 5 km/h). It is easy to verify by substituting the values ​​into relations (4) and (5) that the correct answers are for the locomotive 48 km/h and for a person - 4.(864) km/h(periodic decimal fraction, the result is not very mathematically beautiful).

When the arithmetic mean does not fail

If the problem is formulated as follows: “For equal intervals of time, the body first moved with speed v 1, then v 2, v 3 and so on", a quick answer to the question of how to find the average speed can be found in the wrong way. We will let the reader see this for himself by summing up equal time intervals in the denominator and using in the numerator v avg relation (1). This is perhaps the only case when an erroneous method leads to a correct result. But for guaranteed accurate calculations you need to use the only correct algorithm, invariably turning to the fraction v av = S: t.

Algorithm for all occasions

In order to definitely avoid mistakes, when deciding how to find the average speed, it is enough to remember and follow a simple sequence of actions:

• determine the entire path by summing the lengths of its individual sections;
• set all travel time;
• divide the first result by the second, the unknown quantities not specified in the problem (subject to the correct formulation of the conditions) are reduced.

The article discusses the simplest cases when the initial data are given for equal shares of time or equal sections of the path. In the general case, the ratio of chronological intervals or distances traveled by a body can be very arbitrary (but at the same time mathematically defined, expressed as a specific integer or fraction). Rule for referring to ratio v av = S: t absolutely universal and never fails, no matter how complex algebraic transformations have to be performed at first glance.

Finally, we note: the practical significance of using the right algorithm has not gone unnoticed by observant readers. The correctly calculated average speed in the examples given turned out to be slightly lower than the “average temperature” on the highway. Therefore, a false algorithm for systems that record speeding would mean a greater number of erroneous traffic police decisions sent in “chain letters” to drivers.

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

To calculate the average speed of a trip on a modern car, it is enough to prepare in advance by resetting the daily mileage to zero, as well as resetting the average consumption and speed data. After this, you will be able not to record any time, and also not to think through formulas for calculating the average speed of the trip. However, this option is not always suitable, and not all cars are equipped with a good on-board computer. Therefore, you should figure out how to determine the average speed and other parameters.

We find the average speed and average consumption of the trip in fact

If measuring average travel speed is important to you for commercial purposes or as reporting for the company you work for, then the easiest way is to buy a GPS navigator that has the function of recording speed and time spent on the road. This device will completely replace the on-board computer and will be able to show you the average speed of your trip without using various formulas.

In other cases, more crude determination methods can be used. To take measurements, you will need a stopwatch, which will determine the working time of the trip. That is, every second that the car spends on the road is important to us. Time spent at gas stations or in roadside cafes is often not included in the calculation. The tasks for accurate measurement are as follows:

• before the trip, reset the daily kilometer counter to zero and start a new mileage report;
• Install a stopwatch on the dashboard of your car and don’t forget to turn it on every time you drive off;
• as soon as you stop not because of the traffic situation, but of your own free will, turn off the stopwatch;
• after arriving at your destination, write down the daily meter data accurate to one kilometer;
• also write down the stopwatch data to the nearest minute - this will give you the opportunity to unravel the equation;
• Substitute the obtained data into the formula Vaverage = S / t, where V is the average speed, S is the distance traveled, and t is the time spent on the trip.

Let’s assume that the trip took you exactly 5 hours, and the distance traveled according to the speedometer turned out to be 300 kilometers. This means that the average speed of your car while driving was 60 km/h. If you practice determining the average speed for every long trip, you will be surprised at the low numbers.

It often seems that the average speed should be about 120 kilometers per hour, but in reality it turns out to be less than 60. In a similar way, you can calculate the average fuel consumption. You need to divide the liters spent by hundreds of kilometers of distance traveled. For example, if you drove 300 kilometers, then you need to add 3 liters.

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

Many people wonder what the average speed of a car should really be. Having calculated the amazing fact that the average speed of a car in highway mode was only 80 kilometers per hour, the driver begins to doubt that he is effectively using the vehicle’s resource. In fact, this speed is quite acceptable.

The optimal speed when driving on the highway is 90 km/h, but it is not always possible to maintain cruising speed constantly. Sometimes situations occur that force you to drive slowly for several minutes. For example, you can pull behind a truck, waiting for the opportunity to overtake. The optimal average speed on the highway will depend on the following factors:

• road conditions and the condition of the road along which you travel to your desired location;
• the number of vehicles, congestion and complexity of the route for overtaking slow cars;
• the presence of additional lanes for maneuvers without reducing the speed of the vehicle;
• allowed speed and availability of means of automatic recording of traffic violations or traffic police posts;
• personal safety considerations that come from the condition of one’s own vehicle;
• the type of transport you use to cover the distance, its technical capabilities and limitations;
• weather conditions, the presence of an ice crust on the highway or a wet road that reduces good grip.

These are just the basic factors that affect the average speed of a car during a highway trip. In practice, in the absence of traffic violations, the average speed of a car on the highway is 75-80 kilometers per hour. You can reach an average speed of 90 km/h only on a certain section of the highway. Therefore, do not be upset when you see small values ​​on the on-board computer screen.

The first factor that needs to be assessed when choosing a speed limit on the highway is safety. It is this important criterion that sometimes falls victim to lack of time or the desire to show decent average speed figures. In reality, such goals never lead to good consequences, so always choose safe travel modes.

The optimal speed for the car is the second factor in choosing a travel mode

The main criterion for choosing a speed limit is not the capabilities of the car, but your considerations about the safety and confidence of the trip. If you think that driving at a speed of 90 km/h under these conditions is dangerous, then it is better to choose a more comfortable and confident mode. However, there are certain recommendations from manufacturers.

The first thing worth remembering in this context of conversation is the average consumption. If you maintain the speed of the car at 90 kilometers per hour, then the consumption will be as close as possible to the passport consumption indicators on the highway. Many drivers worry that their car on the highway consumes more fuel than indicated in the documents. This happens for the following reasons:

• when overtaking, the car is forced to consume many times more fuel due to the need for rapid acceleration;
• Constant braking and starting in a traffic jam or on various obstacles also adds to the consumption;
• driving at speeds over 100 kilometers per hour begins to significantly increase gasoline consumption;
• the manufacturer calculates route travel modes at an average speed of 90 kilometers per hour;
• All functions and components of the car, gear ratios and engine are adjusted to this indicator.

It is for these reasons that average consumption figures are often an order of magnitude greater than the passport measurements. When determining fuel consumption in highway mode for the technical characteristics of a car, the manufacturer performs vehicle testing on a track where the car drives at a constant one recommended speed. This is what allows us to achieve such interesting fuel consumption figures.

Let's sum it up

Average vehicle speed is an important indicator that can explain the increased consumption and time delays you experience on a given trip. You need to be able to calculate the average speed and know the operating parameters of your vehicle to select the optimal travel modes. Such knowledge will never hinder you, and will also help you understand many of the subtleties of operating a car.

If you decide to take into account the specifics of your vehicle operation, you should start by taking into account the average speed when driving, as well as average consumption figures. If you can constantly take these indicators into account, you will also be able to improve the average consumption, because in this case the sporting interest will awaken. Do you take into account the average performance of your car?

At school, each of us came across a problem similar to the following. If a car moved part of the way at one speed, and the next part of the road at another, how to find the average speed?

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

Speed ​​in physics is a quantity that describes the amount of distance traveled per unit of time. That is, when they say that a pedestrian’s speed is 5 km/h, this means that he covers a distance of 5 km in 1 hour.

The formula for finding speed looks like this:
V=S/t, where S is the distance traveled, t is time.

There is no single dimension in this formula, since it describes both extremely slow and very fast processes.

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

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

In order not to get confused and not make a mistake in the answer, all quantities are given in the same units of measurement. If the length of the path is indicated in kilometers, and some part of it in centimeters, then until we get unity in dimension, we will not know the correct answer.

Constant speed

Description of the formula.

The simplest case in physics is uniform motion. The speed is constant and does not change throughout the entire journey. There are even speed constants tabulated—unchangeable values. For example, sound travels in air at a speed of 340.3 m/s.

And light is the absolute champion in this regard; it has the highest speed in our Universe - 300,000 km/s. These quantities do not change from the starting point of movement to the final point. They depend only on the medium in which they move (air, vacuum, water, etc.).

Uniform movement often occurs to us in everyday life. This is how a conveyor belt works in a plant or factory, a cable car on mountain roads, an elevator (except for very short periods of start and stop).

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

Uneven speed

Unfortunately, it is extremely rare for things to be so ideal both in life and in physics. Many processes occur at an uneven speed, sometimes speeding up, sometimes slowing down.

Let's imagine the movement of a regular intercity bus. At the beginning of the journey, he accelerates, slows down at traffic lights, or even stops altogether. Then it goes faster outside the city, but slower on the ascents, and accelerates again on the descents.

If you depict this process in the form of a graph, you will get a very intricate line. It is possible to determine the speed from the graph only for a specific point, but there is no general principle.

You will need a whole set of formulas, each of which is suitable only for its own section of the drawing. But there's nothing scary. To describe the movement of the bus, an average value is used.

You can find the average speed using the same formula. Indeed, we know the distance between bus stations and travel time has been measured. Divide one by the other and find the required value.

What is it for?

Such calculations are useful to everyone. We plan our day and movements all the time. Having a dacha outside the city, it makes sense to find out the average ground speed when traveling there.

This will make planning your weekend easier. Having learned to find this value, we can be more punctual and stop being late.

Let's return to the example proposed at the very beginning, when a car drove part of the way at one speed, and the other at a different speed. This type of problem is very often used in the school curriculum. Therefore, when your child asks you to help him with a similar issue, it will be easy for you to do it.

By adding up the lengths of the path sections, you get the total distance. By dividing their values ​​by the speeds indicated in the initial data, you can determine the time spent on each section. Adding them up, we get the time spent on the entire journey.

Remember that speed is given by both a numerical value and a direction. Velocity describes how quickly a body's position changes, as well as the direction in which that body is moving. For example, 100 m/s (south).