How to find the average speed

How to find the average speed? Very simple! It is necessary to divide the whole way into the time that the object of motion was in the way. In other words, it is possible to determine the average velocity as the arithmetic mean of all the velocities of the object's motion. But there are some nuances in solving problems of this direction.

For example, to calculate the average speed, this is a variant of the problem: the traveler first walked at a speed of 4 km per hour for an hour. Then the passing car "picked it up", and the rest of the way he drove in 15 minutes. And the car went at a speed of 60 km per hour. How to determine the average travel speed of a traveler?

Do not just add 4 km and 60 and divide them in half, it will be the wrong move! After all, the paths traveled by foot and by car are unknown to us. So first you need to calculate the whole path.

The first part of the way is easy to find: 4 km per hour X 1 hour = 4 km

With the second part of the way there are small problems: the speed is expressed in hours, and the time of movement is in minutes. This nuance often prevents us from finding the right answer when questions are asked how to find the average speed, path or time.

We will express 15 minutes in hours. To do this, 15 min: 60 min = 0.25 hours. Now we will calculate, what way did the traveler do on the ride?

60 km / h X 0.25 h = 15 km

Now find all the path traveled by the traveler will not be difficult: 15 km + 4 km = 19 km.

The time of motion is also quite easy to calculate. This is 1 hour + 0.25 hours = 1.25 hours.

And now it is already clear how to find the average speed: you need to divide the whole way into the time that the traveler spent on overcoming it. That is, 19 km: 1.25 hours = 15.2 km / hour.

There is such an anecdote in the subject. A man hurrying to the railway station asks the owner of the field: "Can I go to the station through your site? I'm a little late and would like to shorten my path by going directly. Then I definitely have time for the train, which departs at 4:45 pm! "-" Of course, you can cut your way by going through my meadow! And if you notice my bull there, then you will have time even for that train, which departs at 4:15. "

This comic situation, meanwhile, has the most direct relation to such a mathematical concept as the average speed of motion. After all, a potential passenger is trying to cut his way for the simple reason that he knows the average speed of his movement, for example, 5 km per hour. And the pedestrian, knowing that the roundabout along the asphalt road is 7.5 km, making mental calculations, understands that he will need an hour and a half for this road (7.5 km: 5 km / hour = 1.5 hours).

He, having left the house too late, is limited in time, therefore he decides to shorten his path.

And here we are faced with the first rule that dictates to us how to find the average speed of motion: taking into account the direct distance between the extreme points of the path or precisely by calculating the trajectory of the motion. From the above, it is clear to everyone: we should calculate, taking into account the path of the path.

Shortening the path, but not changing its average speed, the object in the person of a pedestrian receives a gain in time. The farmer, assuming the average speed of the "sprinter" escaping from the furious bull, also makes simple calculations and gives his result.

Motorists often use the second, important, rule of calculating the average speed, which refers to the time spent on the road. This concerns the question of how to find the average speed in case the object has during the stopping path.

In this variant, usually, if there are no further clarifications, the calculation takes a full time, including stops. Therefore, the driver can say that his average speed of the morning on the free road is much higher than the average speed in the hour-peak, although the speedometer shows the same figure in both versions.

Knowing these figures, an experienced chauffeur never gets late, assuming in advance what his average speed of movement in the city at different times of the day will be.