Speed is a quantitative characteristic of the movement of the body.
average speed is a physical quantity equal to the ratio of the point displacement vector to the time interval Δt during which this displacement occurred. The direction of the average speed vector coincides with the direction of the displacement vector The average speed is determined by the formula:
Instant Speed, that is, the speed in this moment time is a physical quantity equal to the limit to which the average speed tends with an infinite decrease in the time interval Δt:
In other words, the instantaneous speed at a given moment of time is the ratio of a very small movement to a very small period of time during which this movement occurred.
The instantaneous velocity vector is directed tangentially to the trajectory of the body (Fig. 1.6).
Rice. 1.6. Instantaneous velocity vector.
In the SI system, speed is measured in meters per second, that is, the unit of speed is considered to be the speed of such uniform rectilinear motion, in which in one second the body travels a distance of one meter. The unit of speed is denoted m/s. Often speed is measured in other units. For example, when measuring the speed of a car, train, etc. The commonly used unit of measure is kilometers per hour:
1 km/h = 1000 m / 3600 s = 1 m / 3.6 s
1 m/s = 3600 km / 1000 h = 3.6 km/h
Addition of speeds
The speed of the body in various systems reference connects the classical law of addition of speeds.
body speed relative to fixed frame of reference is equal to the sum of the velocities of the body in moving frame of reference and the most mobile frame of reference relative to the fixed one.
For example, passenger train is moving along the railroad at a speed of 60 km/h. A person is walking along the carriage of this train at a speed of 5 km/h. If we consider the railway to be motionless and take it as a frame of reference, then the speed of a person relative to the frame of reference (that is, relative to railway), will be equal to the addition of the speeds of the train and the person, that is
60 + 5 = 65 if the person is walking in the same direction as the train
60 - 5 = 55 if the person and the train are moving in different directions
However, this is only true if the person and the train are moving along the same line. If a person moves at an angle, then this angle will have to be taken into account, remembering that speed is vector quantity.
Now let's look at the example described above in more detail - with details and pictures.
So, in our case, the railway is fixed frame of reference. The train that is moving along this road is moving frame of reference. The car on which the person is walking is part of the train.
Let's associate the XOY coordinate system with the fixed reference system (Fig. 1.7), and the X P O P Y P coordinate system with the moving reference system (see also the Reference System section). And now let's try to find the speed of a person relative to a fixed frame of reference, that is, relative to the railway.
This displacement addition law. In our example, the movement of a person relative to the railway is equal to the sum of the movements of a person relative to the wagon and the wagon relative to the railway.
Rice. 1.7. The law of addition of displacements.
This is the law speed addition:
The speed of the body relative to the fixed frame of reference is equal to the sum of the velocities of the body in the moving frame of reference and the speed of the moving frame itself relative to the fixed one.
Who do you think moves faster agronomist Vasechkin, Renault car Or a Boeing plane? Which of them will get from Moscow to Krasnodar faster? The answer is obvious. Renault is faster than Vasechkin, but slower than Boeing.
That is, we not only know how different objects move, but we can also compare their speeds. What is speed in physics? How to find the speed of a body, and what are the units of speed?
Speed in physics: how to find speed?
In the 7th grade, the concept of speed is introduced in physics lessons. Without a doubt, all schoolchildren by this moment are already familiar with this word and understand what it means. They also know that speed is measured in km/h. But it is unlikely that they can coherently explain what speed is in physics, what are the units of speed. That is why this seemingly simple concept requires explanation and analysis.
In physics, the speed of movement of Vasechkin, Renault and Boeing is called the speed of their movement. And this speed characterizes which path each of the participants of this journey overcomes per unit of time. And if in flight we will overcome the distance of 1350 kilometers between Moscow and Krasnodar in two hours, by car we will need no less than 15 hours, then on foot the reckless Vasechkin will be able to walk his entire vacation at a brisk pace and arrive at the place only in order to to kiss my mother-in-law, to eat pancakes and to catch a plane to Moscow in order to be in time for work on Monday. Accordingly, per unit of time per hour, the plane will fly 670 kilometers, the car will travel 90 kilometers, and the tourist Vasechkin will wave as many as five kilometers of the road. And then they say that the speed of an airplane is 670 kilometers per hour, a car is 90 kilometers per hour, and a pedestrian is 5 kilometers per hour. That is, the speed is determined by dividing the distance traveled per unit of time by an hour, a minute, or a second.
Speed units
In practice, units such as km / h, m / s and some others are used. They denote speed with the letter v, distance with the letter s, and time with the letter t. Formula for finding speed in physics looks like this: v=(s)/(t).
And if we need to recalculate the speed not in kilometers per hour, but in meters per second, then the recalculation takes place as follows. Since 1 km = 1000 m, and 1 h = 60 min = 3600 s, we can write: 1 km / h = (1000 m) / (3600 s). And then the speed of the aircraft will be equal to: 670 km / h \u003d 670 × (1000 m) / (3600 s) \u003d 186 m / s
In addition to its numerical value, the speed also has a direction, therefore, in the figures, the speed is indicated by an arrow and is called a vector quantity.
Average speed in physics
Let's note one more point. In our example, the driver of the car was driving at a speed of 90 km/h. On the highway, he could drive evenly at that speed for a long time. But passing different cities along the way, he either stopped at traffic lights, then crawled in traffic jams, then dialed in short fits good speed. Those. his speed on different parts of the path was uneven. In this case, the concept of average speed is introduced. Average speed in physics is denoted v_av and is considered the same as the speed with uniform motion. Just take the total travel distance and divide by the total time.
Example 1
For example, a car is moving along a road and there are people in it. They carry out the movement along with the transport on the highway. That is, people move in space relative to the road, but relative to the car itself, people do not move.
From this example it can be seen that, initially, it is necessary to determine the body considered in motion, which in the sciences is called the reference point. The coordinate system is closely interconnected with the method of measuring time, which as a result creates the concept of reference.
Basically, the location of the body is given by a coordinate. Let's analyze one example: the size of a station in orbit near the Earth can be ignored, and only the trajectory of movement can be calculated spaceship while docking at the station. Thus, the dimensions of physical elements can be neglected, and sometimes the body is considered a material point. The line along which the given value moves is called the trajectory, the length of which is called the path. The unit of the path is the meter (m). Mechanical movement is characterized by three physiological quantities: speed, displacement, and acceleration.
The concept of the speed of mechanical movement
Definition 2
Velocity is a physical quantity that is equal to the movement of the body to the time interval during which this interaction occurred.
Mechanical movement is also evaluated by how quickly the body (point) moves. This is the speed of movement. Speed is a concept of a vector quantity. In order to fully set it, it is necessary to establish directly the direction and magnitude of the speed along which it was originally measured. As a rule, the speed of the elements is considered along the trajectory of motion. In this case, the value of the object under study is determined as the path traveled in one unit of time. In other words, to find the correct coefficient of the trajectory of motion, the path of the body must be divided by the time during which it was passed.
Definition 3
Instantaneous speed is the speed of a point at a particular moment in time or at a particular point in the trajectory.
This is a vector physical quantity, numerically equal to the limit to which the average speed rushes in a very small period of time. The indicated trajectory is the first derivative of the vector with respect to time. The instantaneous velocity vector is determined tangentially to the line of motion of the body in the direction of its further movement.
This value gives an accurate idea of the movement of an object at a given time.
For example, during a trip in a car at a certain point in time, the driver looks at the speedometer and sees that the display shows 100 km / h. Then the arrow points to 90 km / h, and after a couple of minutes - 110 km / h.
Remark 1
The value of the instantaneous speed of transport at certain points in time is the received instrument readings.
Is there a physical meaning in the concept of "instantaneous velocity"? This term is characterized by a change in the movement of elements in space. But in order to find out how its location has changed, one should observe the movement over a certain period of time.
Even the most advanced speed measuring devices measure movement over a specific period of time - a finite time interval. The definition of "the speed of the body at the moment" is not considered correct from the point of view of physics. However, it is this thesis that is very convenient in mathematical calculations, so it is used all the time.
The law of addition of speeds
The speed of any physical body relative to a fixed concept of reference is always equal to the vector sum of the movement of elements relative to the moving system. This theory helps to accurately determine the location of an object in a particular period of time.
To understand this law, it is necessary to consider two frames of reference, one of which is associated with a fixed reference point $O$. We denote this concept by $K$, which will be called fixed.
The second system, denoted by $K'$ and moving relative to the body $O$ with the speed $ \bar(u)$ - will be considered as moving.
It must be understood that speed is a vector quantity. It is possible to determine only the direction of the velocity of the vector from the trajectory of motion. The velocity vector is directed tangentially to the trajectory along which the body passes, which is currently moving.
Negative speed
Remark 2
The speed of the body can be negative in the case when the body moves in the opposite direction from the coordinate axis in the selected frame of reference.
A British scientist, Roberta Boyd, was able to assign a "negative" speed to the beam of light, at which the peak of the pulse moved towards the source, and not away from it. Interestingly, if you change the medium in a special way and pass light through it, it is possible to easily control the speed of the light pulse - "freezing" or slowing it down tens of thousands of times, or even stopping it altogether.
In this aspect, we are talking about the group velocity, which determines the propagation speed of one beam of light pulses. Due to scattering, this element can move several orders of magnitude slower than each individual photon, and vice versa - faster than the speed of light in vacuum.
IN this case we are not talking about a violation of the laws of nature, because the very first photons in the impulse reach the end, not " faster than light". In the case of stopping the light beam, it is necessary to speak about the absorption of the pulse by the prepared medium with re-emission. This saves all important parameters the original object, "to the last photon."
Who do you think moves faster, the agronomist Vasechkin, a Renault car or a Boeing plane? Which of them will get from Moscow to Krasnodar faster? The answer is obvious. Renault is faster than Vasechkin, but slower than Boeing.
That is, we not only know how different objects move, but we can also compare their speeds. What is speed in physics? How to find the speed of a body, and what are the units of speed?
Speed in physics: how to find speed?
In the 7th grade, the concept of speed is introduced in physics lessons. Without a doubt, all schoolchildren by this moment are already familiar with this word and imagine what it means.
- They also know that speed is measured in km/h and is denoted by the letter V.
But it is unlikely that they can coherently explain what speed is in physics, what are the units of speed. That is why this seemingly simple concept requires explanation and analysis.
In physics, the speed of movement of Vasechkin, Renault and Boeing called their speed. And this speed characterizes which path each of the participants of this journey overcomes per unit of time. And if in flight we will overcome the distance of 1350 kilometers between Moscow and Krasnodar in two hours, by car we will need no less than 15 hours, then on foot the reckless Vasechkin will be able to walk his entire vacation at a brisk pace and arrive at the place only in order to to kiss my mother-in-law, to eat pancakes and to catch a plane to Moscow in order to be in time for work on Monday.
Accordingly, per unit of time per hour, the plane will fly 670 kilometers, the car will travel 90 kilometers, and the tourist Vasechkin will wave as many as five kilometers of the road. And then they say that the speed of an airplane is 670 kilometers per hour, a car is 90 kilometers per hour, and a pedestrian is 5 kilometers per hour. That is, the speed is determined by dividing the distance traveled per unit of time by an hour, a minute, or a second.
Speed units
In practice, units such as km / h, m / s and some others are used. They denote speed with the letter v, distance with the letter s, and time with the letter t. Formula for finding speed in physics looks like that:
- V = s / t,
Where s is the distance traveled
t is the time taken to overcome this path
And if we need to recalculate the speed not in kilometers per hour, but in meters per second, then the recalculation takes place as follows. Since 1 km = 1000 m, and 1 h = 60 min = 3600 s, we can write: 1 km / h = (1000 m) / (3600 s). And then the speed of the aircraft will be equal to: 670 km / h \u003d 670 × (1000 m) / (3600 s) \u003d 186 m / s
In addition to its numerical value, the speed also has a direction, therefore, in the figures, the speed is indicated by an arrow and is called a vector quantity.
Average speed in physics
Let's note one more point. In our example, the driver of the car was driving at a speed of 90 km/h. On the highway, he could drive evenly at that speed for a long time. But passing through different cities along the way, he either stopped at traffic lights, crawled in traffic jams, or picked up a good speed in short bursts.
Those. his speed on different parts of the path was uneven. In this case, the concept of average speed is introduced. The average speed in physics is denoted by V _av and is considered the same as the speed with uniform motion. Just take the total travel distance and divide by the total time.
Speed is one of the main characteristics. It expresses the very essence of movement, i.e. determines the difference that exists between a stationary body and a moving body.
The SI unit for speed is m/s.
It is important to remember that speed is a vector quantity. The direction of the velocity vector is determined by the movement. The velocity vector is always directed tangentially to the trajectory at the point through which the moving body passes (Fig. 1).
For example, consider the wheel of a moving car. The wheel rotates and all points of the wheel move in circles. Spray flying from the wheel will fly along tangents to these circles, indicating the direction of the velocity vectors of the individual points of the wheel.
Thus, the speed characterizes the direction of motion of the body (the direction of the velocity vector) and the speed of its movement (modulus of the velocity vector).
Negative speed
Can the speed of a body be negative? Yes maybe. If the speed of the body is negative, this means that the body is moving in the direction opposite to the direction of the coordinate axis in the selected frame of reference. Figure 2 shows the movement of the bus and the car. The speed of the car is negative and the speed of the bus is positive. It should be remembered that speaking of the sign of the velocity, we mean the projection of the velocity vector onto the coordinate axis.
Uniform and uneven movement
IN general case speed depends on time. According to the nature of the dependence of speed on time, the movement is uniform and uneven.
DEFINITION
Uniform movement is a movement with a constant modulo speed.
In the case of uneven movement, they talk about:
Examples of solving problems on the topic "Speed"
EXAMPLE 1
| Exercise | The car passed the first half of the way between two settlements at a speed of 90 km/h, and the other half at a speed of 54 km/h. Determine average speed car. |
| Solution | It would be incorrect to calculate the average speed of a car as the arithmetic mean of the two indicated speeds. Let's use the definition of average speed: Since a straight line is assumed uniform motion, vector signs can be omitted. The time spent by the car on the passage of the entire segment of the path: where is the time taken to complete the first half of the journey, and is the time taken to complete the second half of the journey. The total displacement is equal to the distance between settlements, i.e. . Substituting these ratios into the formula for the average speed, we get: We translate the speeds in individual sections into the SI system: Then the average speed of the car is: |
| Answer | The average speed of the car is 18.8 m/s |
EXAMPLE 2
| Exercise | A car travels for 10 seconds at a speed of 10 m/s and then travels for another 2 minutes at a speed of 25 m/s. Determine the average speed of the car. |
| Solution | Let's make a drawing. |
