Formula for calculating time. How to find speed. The concept of a physical quantity and formula.

28.01.2019 Education

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.

Time, distance? Let's start with speed. Look closely, what is it measured in? Naturally, km/h, m/s. There are other units of measurement, for example, km / s (in astronautics), mm / h (in biochemistry). Notice what comes before and after the "/" sign. Firstly, it means "fraction", which means that in the numerator - mm, km, m, in the denominator - h, s, min. Secondly, it seems like a formula, doesn't it? Kilometers, meters - distance, length, and hour, second, minute - time. Here's a hint for you. To make it easier to remember how to find the speed, look not at the units of measurement (km / h, m / s). In one word:

Time

What is time? Of course, it depends on the speed. For example, you are waiting at the doorstep of your mother and older brother. They are coming from the store. My brother arrived much earlier. Mom had to wait another 5 minutes. Why? Because they were moving at different speeds. Of course, in order to get to your destination faster, you need to add speed: speed up your pace, put more pressure on the "gas" in the car, accelerate on a bicycle. Only when in a hurry, be careful and vigilant so as not to crash into someone or something.

Speed has a clue - km/h. But what about with time? First, time is measured in minutes, seconds, hours. The formula "speed, time, distance" here is transformed as follows:

time t[sec., min., h]=S[m, mm, km]/v[m/s, mm/min, km/h].

If you convert the fraction according to all the rules of mathematics, reduce the distance (length) parameter, then only a second, minute or hour will remain.

Distance, distance traveled

It will be easier to navigate here, most likely for motorists who have a odometer in the car. They will be able to determine how many kilometers they have traveled, and they also know the speed. But since the movement is uneven, it will not be possible to set the exact time of movement, if only we take

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.

All tasks in which there is movement of objects, their movement or rotation, are somehow connected with speed.

This term characterizes the movement of an object in space over a certain period of time - the number of units of distance per unit of time. He is a frequent "guest" of both sections of mathematics and physics. The original body can change its location both uniformly and with acceleration. In the first case, the speed is static and does not change during the movement, in the second, on the contrary, it increases or decreases.

How to find speed - uniform motion

If the speed of the body remained unchanged from the beginning of the movement to the end of the path, then we are talking about moving with constant acceleration - uniform motion. It can be straight or curved. In the first case, the trajectory of the body is a straight line.

Then V=S/t, where:

V is the desired speed,
S - distance traveled (total path),
t is the total time of movement.

How to find speed - acceleration is constant

If an object was moving with acceleration, then its speed changed as it moved. In this case, the expression will help to find the desired value:

V \u003d V (beginning) + at, where:

V (beginning) - the initial speed of the object,
a is the acceleration of the body,
t is the total travel time.

How to find speed - uneven motion

IN this case there is a situation when the body passes different parts of the path in different times.
S(1) - for t(1),
S(2) - for t(2), etc.

On the first section, the movement took place at a “tempo” V(1), on the second - V(2), and so on.

To find out the speed of an object moving all the way (its average value), use the expression:

V= (S(1)+S(2))/(t(1)+t(2)).

How to find speed - rotation of an object

In the case of rotation, we are talking about the angular velocity, which determines the angle through which the element rotates per unit of time. The desired value is denoted by the symbol ω (rad / s).

ω = Δφ/Δt, where:

Δφ – passed angle (angle increment),
Δt - elapsed time (movement time - time increment).

If the rotation is uniform, the desired value (ω) is associated with such a concept as the period of rotation - how long will it take for our object to make 1 complete revolution. In this case:

ω = 2π/T, where:
π is a constant ≈3.14,
T is the period.

Or ω = 2πn, where:
π is a constant ≈3.14,
n is the frequency of circulation.

With the known linear speed of the object for each point on the path of motion and the radius of the circle along which it moves, to find the speed ω it will be required following expression:

ω = V/R, where:
V is the numerical value of the vector quantity (linear velocity),
R is the radius of the body's trajectory.

How to find speed - approaching and moving away points

In such tasks, it would be appropriate to use the terms approach speed and distance speed.

If the objects are heading towards each other, then the speed of approach (retreat) will be as follows:
V (approach) = V(1) + V(2), where V(1) and V(2) are the velocities of the corresponding objects.

If one of the bodies catches up with the other, then V (approach) = V (1) - V (2), V (1) is greater than V (2).

How to find speed - movement on a body of water

If events unfold on the water, then the speed of the current (i.e., the movement of water relative to a fixed shore) is added to the object’s own speed (movement of the body relative to the water). How are these concepts related?

In the case of moving downstream, V=V(own) + V(tech).
If against the current - V \u003d V (own) - V (flow).

The concept of time reflects such properties of the world as constant development, its change in the human mind. The processes go in a certain sequence, while they have a certain duration.

Definition

Time- a physical quantity that reflects the property of material processes to have a certain duration, follow each other in an established sequence and develop in stages. The time is denoted by the letter t.

Features of time as a physical quantity

Time is inseparable from matter and its movement, as it is its form of existence. It makes no sense to talk about time in itself, because apart from material processes, the flow of time becomes meaningless. Only the study of the processes taking place in the material world and their interrelations makes the concept of time physically meaningful.

In a series of processes occurring in nature, a special place is occupied by repetitive processes (the repetition of days and nights, breathing, the movement of stars across the sky, etc.). The study and comparison of similar processes with each other leads to the idea of the duration of material processes, the comparison of their duration leads to the idea of their measurement.

The measurement standard is a periodic process, which is called a clock. There are reference systems in which it is possible to introduce a single time with sufficient accuracy for practice. The introduction of common time is well confirmed by experiment. The theory makes it possible to predict deviations of the common time, which can be verified empirically.

The duration of the physical process that occurs at a certain point is determined using a clock that is located at the same point. In this case, direct comparison is used, the durations of processes that flow at one point are compared. The measurement of duration is reduced to fixing the beginning and end of the process under consideration on the scale of the process, which is taken as a reference. In this case, they speak of fixing the clock readings at the time of the beginning and end of the process, and this has nothing to do with the actual location of the clock (process) at the point of consideration.

Clock synchronization and the study of the laws of propagation of physical signals developed in parallel, while mutual refinements and additions took place. Synchronization is carried out using signals that propagate at a finite speed. This method uses the definition of constant speed: if a signal comes from the point where the clock shows t 0 , moving at a speed v=const, then when the signal arrives at a point at a distance s, the clock at this point should show the time.

Definition

instantaneous speed(or more often just speed) of a material point is a physical quantity equal to the first derivative of the radius-vector of the point with respect to time (t). Speed is usually denoted by the letter v. This is a vector quantity. Mathematically, the definition of the instantaneous velocity vector is written as:

The speed has a direction indicating the direction of movement of a material point and lies on a tangent to the trajectory of its movement. The modulus of speed can be defined as the first derivative of the path length (s) with respect to time:

Speed characterizes the speed of movement in the direction of movement of the point in relation to the considered coordinate system.

Speed in different coordinate systems

Velocity projections on the axes of the Cartesian coordinate system will be written as:

Therefore, the velocity vector in Cartesian coordinates can be represented as:

where are the unit vectors. In this case, the modulus of the velocity vector is found using the formula:

In cylindrical coordinates, the velocity modulus is calculated using the formula:

in the spherical coordinate system:

Special cases of formulas for calculating speed

If the speed module does not change in time, then such a movement is called uniform (v=const). With uniform motion, the speed can be calculated using the formula:

where s is the length of the path, t is the time it takes the material point to cover the path s.

In accelerated motion, the speed can be found as: