# Uniformly accelerated motion. Tasks and formulas

The most important characteristic of body movement is its speed. Knowing it, as well as some other parameters, we can always determine the time of movement, the distance traveled, the initial, final speed and acceleration. Equally accelerated motion is only one type of motion. It usually occurs in problems in physics from the kinematics section. In such tasks, the body is taken as a material point, which greatly simplifies all calculations.

## Speed. Acceleration

First of all, I would like to draw the reader’s attention to the fact that these two physical quantities are not scalar, but vectorial. And this means that when solving a certain kind of tasks, it is necessary to pay attention to what kind of acceleration the body has in terms of the sign, as well as what is the vector of the speed of the body itself. In general, in moments of an exclusively mathematical plan, such moments are omitted, but in physics, this is quite important, because in kinematics, because of one incorrectly given sign, the answer can beerroneous.

## Examples

As an example, it is possible to take uniformly accelerated and equally slow motion. The uniformly accelerated motion is characterized, as is well known, by the acceleration of the body. Acceleration remains constant, but the speed is continuously increasing at every single point in time. And with equally slow motion, the acceleration has a negative value, the speed of the body continuously decreases. These two types of acceleration are the basis of many physical problems and are quite often encountered in the problems of the first part of tests in physics.

## Example of uniformly accelerated motion

Equally accelerated movement we meet every day everywhere. No car moves evenly in real life. Even if the speedometer shows exactly 6 kilometers per hour, it should be understood that this is not really the case. Firstly, if we take this question from a technical point of view, the first parameter that will give an inaccuracy will be the device. Rather, its error.

We meet them in all instrumentation. The same line. Take about ten pieces at least the same (15 centimeters, for example) rulers, although different (15, 30, 45, 50 centimeters).Attach them to each other, and you will notice that there are small inaccuracies, and their scales do not quite match. This is the error. In this case, it will be equal to half the price of division, as with other instruments that produce certain values.

The second factor that will give inaccuracy is the scale of the device. The speedometer does not take into account values such as half a kilometer, one second kilometer, and so on. To notice on the device is an eye hard enough. Almost impossible. But there is a change in speed. Let on such a small amount, but still. Thus, it will be a uniformly accelerated motion, not a uniform one. The same can be said about the usual step. Let's go, let's say, we walk, and someone says: our speed is 5 kilometers per hour. But this is not entirely true, and why, it was told a little higher.

## Acceleration of the body

Acceleration can be positive and negative. This was mentioned earlier. We add that acceleration is a vector quantity that is numerically equal to the change in speed over a certain period of time. That is, through the formula, it can be designated as follows: a = dV / dt, where dV is the change in speed, dt is the time interval (change in time).

## Nuances

Immediately, a question may arise about how acceleration in this situation can be negative.Those people who ask a similar question are motivated by the fact that even the speed cannot be negative, not that time. In fact, time cannot really be negative. But it is often forgotten that the speed can take on negative values. This is a vector quantity, do not forget about it! The whole thing, probably, in stereotypes and incorrect thinking.

So, to solve problems it is enough to understand one thing: the acceleration will be positive if the body accelerates. And it will be negative if the body slows down. That's all, simple enough. The simplest logical thinking or the ability to see between the lines will already be, in fact, part of the solution of a physical problem related to speed and acceleration. A special case is the acceleration of free fall, and it cannot be negative.

## Formulas. Problem solving

It should be understood that the tasks related to speed and acceleration are not only practical, but also theoretical. Therefore, we will analyze them and, if possible, we will try to explain why this or that answer is correct or, on the contrary, wrong.

## Theoretical problem

Very often in exams in physics in the 9th and 11th grades one can meet such questions: “How will the body behave if the sum of all forces acting on it is zero?”. In fact, the wording of the question may be very different, but the answer is still the same. Here, the first thing to do is to start up surface buildings and ordinary logical thinking.

The choice of the student is given 4 answers. First: “the speed will be zero”. The second: “the speed of the body decreases over a period of time”. Third: “the speed of the body is constant, but it is not exactly zero”. Fourth: “speed can have any value, but at each moment of time it will be constant”.

The correct answer here is, of course, the fourth. Now let's see why. Let's try to consider all the options in turn. As is known, the sum of all forces acting on a body is the product of mass and acceleration. But the mass remains constant, we discard it. That is, if the sum of all forces is zero, the acceleration will also be zero.

So, assume that the speed will be zero. But this can not be, since we have zero acceleration.Purely physically, this is permissible, but not in this case, since now we are talking about something else. Let the speed of the body decrease over a period of time. But how can it decrease, if the acceleration is constant, and it is zero? There are no reasons and prerequisites for decreasing or increasing speed. Therefore, we reject the second option.

Suppose that the velocity of the body is constant, but it is not exactly zero. It really will be constant due to the fact that the acceleration is simply absent. But it is impossible to say for sure that the speed will be different from zero. But the fourth option - right in the apple. The speed can be any, but since the acceleration is absent, it will be constant in time.

## Practical task

Determine which path the body traveled in a specific time period t1-t2 (t1 = 0 seconds, t2 = 2 seconds) if the following data is available. The initial speed of the body in the interval from 0 to 1 second is 0 meters per second, the final speed is 2 meters per second. The speed of the body as of time 2 seconds is also equal to 2 meters per second.

Solving a similar problem is quite simple, you just need to catch its essence. So, you need to find a way.Well, let's start looking for it, first selecting two areas. It is easy to see that the first part of the path (from 0 to 1 second) the body passes evenly accelerated, as evidenced by the increase in its speed. Then we will find this acceleration. It can be expressed as the difference of speeds divided by the time of movement. The acceleration will be (2-0) / 1 = 2 meters per second squared.

Accordingly, the distance traveled on the first leg of the path S will be equal to: S = V0t + at ^ 2/2 = 0 * 1 + 2 * 1 ^ 2/2 = 0 + 1 = 1 meter. In the second part of the path in the period from 1 second to 2 seconds, the body moves evenly. Hence, the distance will be equal to V * t = 2 * 1 = 2 meters. Now we sum up the distances, we get 3 meters. This is the answer.