1. Acceleration is a quantity that characterizes the change in speed per unit time. Knowing the acceleration of a body and its initial speed, you can find the speed of the body at any moment in time.

2. With any uneven movement, the speed changes. How does acceleration characterize this change?

2. If the acceleration of a body in magnitude is large, this means that the body quickly gains speed (when it accelerates) or quickly loses it (when braking).

3. How does “slow” linear motion differ from “accelerated” motion?

3. Movement with increasing absolute speed is called “accelerated” movement. Movement with decreasing speed in “slow” motion.

4. What is uniformly accelerated motion?

4. The movement of a body in which its speed changes equally over any period of time is called equal accelerated movement.

5. Can a body move at high speed but with low acceleration?

5. Maybe. Since acceleration does not depend on the value of speed, but characterizes only its change.

6. What is the direction of the acceleration vector during rectilinear uneven motion?

6. In case of rectilinear uneven motion, the acceleration vector a lies on the same straight line with the vectors V 0 and V .

7. Speed ​​is a vector quantity, and both the magnitude of the speed and the direction of the speed vector can change. What exactly changes during rectilinear uniformly accelerated motion?

7. Speed ​​module. Since the vectors V and a lie on the same line and the signs of their projections coincide.

The acceleration of a point is a spatiotemporal measure of the change in motion. It characterizes the speed and direction of change in the velocity vector of a point in this moment time. Acceleration is measured by the limit of the ratio of the change in speed to the corresponding period of time (in a given frame of reference), when this period tends to zero: a=lim Dv / Dt

The speed of a point as a vector can change modulo, By direction or simultaneously both in modulus and direction. Accordingly, they distinguish point acceleration:

A ) positive, which has the same direction as the speed, the speed increases; b) negative, having the opposite direction to the direction speed, - speed decreases; V ) normal- its direction is perpendicular to the direction of speed and the speed vector changes only the direction without changing its magnitude (curvilinear motion).

During forward movement linear acceleration of the body equal to the linear acceleration of any point.

During rotational motion, positive and negative acceleration, directed tangentially, are called tangential, and those directed along the radius (normals) - radial or normal. Each of these accelerations can occur independently. Combination tangential acceleration with normal it happens when the speed changes both in magnitude and direction. Vector sum normal and tangential acceleration determines complete acceleration.

During rotational movement angular acceleration of body characterizes the change in rotation speed.

Angular acceleration is a measure of the change in the speed of rotational motion of a body at a given moment in time. Angular acceleration is defined as the limit of the ratio of change angular velocity to the corresponding period of time in a given reference system1, when this period tends to zero:

The average acceleration during the entire movement, especially in cases where it changes sign, is usually not determined, since it does not characterize the details of the movement.

The angular acceleration can be either positive(acceleration of rotation), or negative(rotation slowdown). For rotating solid the ratios of linear accelerations of points to their radii of rotation (distances to the axis) are the same; they are equal to the angular acceleration of the body: a/r=e

The linear acceleration of a point on a rotating body is equal to the product of the angular acceleration and the radius of rotation: a=er (in radian dimension);

IN complex movement body (simultaneously translational and rotational) changes in speed are measured linear acceleration BCT and the angular acceleration of the body relative to its BCT.

Definition angular accelerations biomechanical system even more difficult than determining angular velocities.

Thus, acceleration characterizes the variability of speed.

The velocities of points on the links of the human body change in magnitude and direction. This means that there are always normal accelerations and almost always tangential (positive and negative). There are no movements of the human body without accelerations, but the accelerations can sometimes be so small that they make virtually no difference.

Acceleration is a quantity that characterizes the rate of change in speed.

For example, when a car starts moving, it increases its speed, that is, it moves faster. At first its speed is zero. Once moving, the car gradually accelerates to a certain speed. If a red traffic light comes on on its way, the car will stop. But it will not stop immediately, but over time. That is, its speed will decrease down to zero - the car will move slowly until it stops completely. However, in physics there is no term “slowdown”. If a body moves, slowing down, then this will also be an acceleration of the body, only with a minus sign (as you remember, speed is vector quantity).

> is the ratio of the change in speed to the period of time during which this change occurred. The average acceleration can be determined by the formula:

Rice. 1.8. Average acceleration. In SI acceleration unit– is 1 meter per second per second (or meter per second squared), that is

Meter per second squared equal to acceleration rectilinearly moving point, in which in one second the speed of this point increases by 1 m/s. In other words, acceleration determines how much the speed of a body changes in one second. For example, if the acceleration is 5 m/s2, then this means that the speed of the body increases by 5 m/s every second.

Instantaneous acceleration of the body ( material point) at this moment in time is physical quantity, equal to the limit, to which the average acceleration tends as the time interval tends to zero. In other words, this is the acceleration that the body develops in a very short period of time:

With accelerated straight motion the speed of the body increases in absolute value, that is

V 2 > v 1

and the direction of the acceleration vector coincides with the velocity vector

If the speed of a body decreases in absolute value, that is

V 2< v 1

then the direction of the acceleration vector is opposite to the direction of the velocity vector. In other words, in in this case is happening slowing down, in this case the acceleration will be negative (and< 0). На рис. 1.9 показано направление векторов ускорения при прямолинейном движении тела для случая ускорения и замедления.

Rice. 1.9. Instant acceleration.

When driving along curvilinear trajectory Not only the magnitude of the velocity changes, but also its direction. In this case, the acceleration vector is represented as two components (see the next section).

Tangential (tangential) acceleration– this is the component of the acceleration vector directed along the tangent to the trajectory at a given point of the movement trajectory. Tangential acceleration characterizes the change in speed modulo at curvilinear movement.

Rice. 1.10. Tangential acceleration.

The direction of the tangential acceleration vector (see Fig. 1.10) coincides with the direction linear speed or the opposite of it. That is, the tangential acceleration vector lies on the same axis with the tangent circle, which is the trajectory of the body.

Normal acceleration

Normal acceleration is the component of the acceleration vector directed along the normal to the trajectory of motion at a given point on the trajectory of the body. That is, the normal acceleration vector is perpendicular to the linear speed of movement (see Fig. 1.10). Normal acceleration characterizes the change in speed in direction and is denoted by the letter. The normal acceleration vector is directed along the radius of curvature of the trajectory.

Full acceleration

Full acceleration during curvilinear movement, it consists of tangential and normal acceleration by and is determined by the formula:

(according to the Pythagorean theorem for a rectangular rectangle).

In this topic we will look at a very special type of irregular motion. Based on the opposition to uniform motion, uneven movement- this is movement at unequal speed along any trajectory. What is the peculiarity of uniformly accelerated motion? This is an uneven movement, but which "equally accelerated". We associate acceleration with increasing speed. Let's remember the word "equal", we get an equal increase in speed. How do we understand “equal increase in speed”, how can we evaluate whether the speed is increasing equally or not? To do this, we need to record time and estimate the speed over the same time interval. For example, a car starts to move, in the first two seconds it develops a speed of up to 10 m/s, in the next two seconds it reaches 20 m/s, and after another two seconds it already moves at a speed of 30 m/s. Every two seconds the speed increases and each time by 10 m/s. This is uniformly accelerated motion.

The physical quantity that characterizes how much the speed increases each time is called acceleration.

Can the movement of a cyclist be considered uniformly accelerated if, after stopping, in the first minute his speed is 7 km/h, in the second - 9 km/h, in the third - 12 km/h? It is forbidden! The cyclist accelerates, but not equally, first he accelerated by 7 km/h (7-0), then by 2 km/h (9-7), then by 3 km/h (12-9).

Typically, movement with increasing speed is called accelerated movement. Movement with decreasing speed is slow motion. But physicists call any movement with changing speed accelerated movement. Whether the car starts moving (the speed increases!) or brakes (the speed decreases!), in any case it moves with acceleration.

Uniformly accelerated motion- this is the movement of a body in which its speed for any equal intervals of time changes(can increase or decrease) the same

Body acceleration

Acceleration characterizes the rate of change in speed. This is the number by which the speed changes every second. If the acceleration of a body is large in magnitude, this means that the body quickly gains speed (when it accelerates) or quickly loses it (when braking). Acceleration is a physical vector quantity, numerically equal to the ratio changes in speed to the period of time during which this change occurred.

Let's determine the acceleration in the next problem. IN starting moment time, the speed of the ship was 3 m/s, at the end of the first second the speed of the ship became 5 m/s, at the end of the second - 7 m/s, at the end of the third 9 m/s, etc. Obviously, . But how did we determine? We are looking at the speed difference over one second. In the first second 5-3=2, in the second second 7-5=2, in the third 9-7=2. But what if the speeds are not given for every second? Such a problem: the initial speed of the ship is 3 m/s, at the end of the second second - 7 m/s, at the end of the fourth 11 m/s. In this case, you need 11-7 = 4, then 4/2 = 2. We divide the speed difference by the time interval.

This formula is most often used in a modified form when solving problems:

The formula is not written in vector form, so we write the “+” sign when the body is accelerating, the “-” sign when it is slowing down.

Acceleration vector direction

The direction of the acceleration vector is shown in the figures

In this figure, the car moves in a positive direction along the Ox axis, the velocity vector always coincides with the direction of movement (directed to the right). When the acceleration vector coincides with the direction of the speed, this means that the car is accelerating. Acceleration is positive.

During acceleration, the direction of acceleration coincides with the direction of speed. Acceleration is positive.

In this picture, the car is moving in the positive direction along the Ox axis, the velocity vector coincides with the direction of movement (directed to the right), the acceleration does NOT coincide with the direction of the speed, this means that the car is braking. Acceleration is negative.

When braking, the direction of acceleration is opposite to the direction of speed. Acceleration is negative.

Let's figure out why the acceleration is negative when braking. For example, in the first second the motor ship dropped its speed from 9m/s to 7m/s, in the second second to 5m/s, in the third to 3m/s. The speed changes to "-2m/s". 3-5=-2; 5-7=-2; 7-9=-2m/s. This is where it comes from negative meaning acceleration.

When solving problems, if the body slows down, acceleration is substituted into the formulas with a minus sign!!!

Moving during uniformly accelerated motion

An additional formula called timeless

Formula in coordinates

Medium speed communication

At uniformly accelerated motion the average speed can be calculated as the arithmetic mean of the initial and final speeds

From this rule follows a formula that is very convenient to use when solving many problems

Path ratio

If a body moves uniformly accelerated, the initial speed is zero, then the paths traversed in successive equal intervals of time are related as a successive series of odd numbers.

The main thing to remember

1) What is uniformly accelerated motion;
2) What characterizes acceleration;
3) Acceleration is a vector. If a body accelerates, the acceleration is positive, if it slows down, the acceleration is negative;
3) Direction of the acceleration vector;
4) Formulas, units of measurement in SI

Exercises

Two trains are moving towards each other: one is heading north at an accelerated rate, the other is moving slowly to the south. How are train accelerations directed?

Equally to the north. Because for the first train the acceleration coincides in direction with the movement, and for the second - opposite movement(he slows down).

For example, a car that starts moving moves faster as it increases its speed. At the point where the motion begins, the speed of the car is zero. Having started moving, the car accelerates to a certain speed. If you need to brake, the car will not be able to stop instantly, but over time. That is, the speed of the car will tend to zero - the car will begin to move slowly until it stops completely. But physics does not have the term “slowdown”. If a body moves, decreasing speed, this process is also called acceleration, but with a “-” sign.

Medium acceleration is called the ratio of the change in speed to the period of time during which this change occurred. Calculate the average acceleration using the formula:

where is it . The direction of the acceleration vector is the same as the direction of change in speed Δ = - 0

where 0 is initial speed. At a moment in time t 1(see figure below) at the body 0. At a moment in time t 2 the body has speed. Based on the rule of vector subtraction, we determine the vector of speed change Δ = - 0. From here we calculate the acceleration:

.

In the SI system unit of acceleration called 1 meter per second per second (or meter per second squared):

.

A meter per second squared is the acceleration of a rectilinearly moving point, at which the speed of this point increases by 1 m/s in 1 second. In other words, acceleration determines the degree of change in the speed of a body in 1 s. For example, if the acceleration is 5 m/s2, then the speed of the body increases by 5 m/s every second.

Instantaneous acceleration of a body (material point) at a given moment in time is a physical quantity that is equal to the limit to which the average acceleration tends as the time interval tends to 0. In other words, this is the acceleration developed by the body in a very small segment time:

.

Acceleration has the same direction as the change in speed Δ in extremely short periods of time during which the speed changes. The acceleration vector can be specified using projections onto the corresponding coordinate axes in given system reference (projections a X, a Y, a Z).

With accelerated linear motion, the speed of the body increases in absolute value, i.e. v 2 > v 1 , and the acceleration vector has the same direction as the velocity vector 2 .

If the speed of a body decreases in absolute value (v 2< v 1), значит, у вектора ускорения направление противоположно направлению вектора скорости 2 . Другими словами, в таком случае наблюдаем slowing down(acceleration is negative, and< 0). На рисунке ниже изображено направление векторов ускорения при прямолинейном движении тела для случая ускорения и замедления.

If movement occurs along a curved path, then the magnitude and direction of the speed changes. This means that the acceleration vector is depicted as two components.

Tangential (tangential) acceleration they call that component of the acceleration vector that is directed tangentially to the trajectory at a given point of the trajectory of movement. Tangential acceleration describes the degree of change in speed modulo during curvilinear motion.

U tangential acceleration vectorτ (see figure above) the direction is the same as that of linear speed or opposite to it. Those. the tangential acceleration vector is in the same axis with the tangent circle, which is the trajectory of the body.