Tc 2 linear uniformly accelerated motion option 1. Rectilinear uniform motion
There are different types of mechanical movement. Depending on the shape of the trajectory, the movement can be rectilinear or curved. When moving, the speed of a body can remain constant or change over time. Depending on the nature of the speed change, the movement will be uniform or uneven.
Rectilinear movement is a movement in which the trajectory of a body (point) is a straight line. For example, driving a car along a section of road that has no ups, downs, or turns.
Uniform rectilinear motion is a motion in which a body travels the same paths over any equal periods of time and the direction of motion does not change. I.
If we compare the uniform motion of several bodies, we can note that the speed of change in their position in space can be different, which is characterized by a physical quantity called speed.
Speed of uniform linear motion called a vector physical quantity equal to the ratio of the movement of a body to the time during which this movement occurred.
(1)
The SI unit of speed is meters per second (1m/c). The unit of speed is taken to be the speed of such uniform motion at which the body is 1 With makes a move 1 m.
In rectilinear uniform motion, the speed does not change over time.
Knowing the speed of uniform motion, you can find the displacement of the body over any period of time:
(2)
With uniform rectilinear motion, the velocity and displacement vectors are directed in one direction.
The main task of mechanics is to determine the position of a body at any moment in time, that is, to determine its coordinates. The equation of motion is the dependence of the coordinates of a body on time during uniform rectilinear motion.
The body has moved 
. Let's direct the X coordinate axis in the direction of body movement. x 0
– initial coordinate of the body, x– final coordinate of the body.
Thus, the coordinate of a body during uniform rectilinear motion at any time can be determined if its initial coordinate and the projection of the speed of movement onto the axis are known X. Projections of velocity and displacement can be either positive or negative.
The graph of the modulus of the velocity vector versus time for uniform motion is a straight line parallel to the abscissa axis. Indeed, over time, the speed during such movement remains constant.
Graph of body speed versus time with uniform motion V=const
In case of rectilinear uniform motion, the magnitude of the displacement vector is numerically equal to the area under the graph of displacement to the time axis.
The graph of the displacement of a body versus time during rectilinear uniform motion is a straight line passing through the origin of coordinates. Moreover, the steeper the movement graph, the greater the speed of the body.
Graph of the distance traveled by a body versus time
In case of rectilinear uniform motion, the magnitude of the velocity vector is numerically equal to the tangent of the angle of inclination of the displacement graph to the time axis.
Since the dependence of the body coordinates on time is a linear function, the corresponding dependence graph (motion graph) is a straight line. An example of constructing such a graph is shown in the figure.
Graph of body coordinates versus time
Uniform movement– this is movement at a constant speed, that is, when the speed does not change (v = const) and acceleration or deceleration does not occur (a = 0).
Straight-line movement- this is movement in a straight line, that is, the trajectory of rectilinear movement is a straight line.
Uniform linear movement- this is a movement in which a body makes equal movements at any equal intervals of time. For example, if we divide a certain time interval into one-second intervals, then with uniform motion the body will move the same distance for each of these time intervals.
The speed of uniform rectilinear motion does not depend on time and at each point of the trajectory is directed in the same way as the movement of the body. That is, the displacement vector coincides in direction with the velocity vector. In this case, the average speed for any period of time is equal to the instantaneous speed:
V cp = v
Distance traveled in linear motion is equal to the displacement module. If the positive direction of the OX axis coincides with the direction of movement, then the projection of the velocity onto the OX axis is equal to the magnitude of the velocity and is positive:
V x = v, that is v > 0
The projection of displacement onto the OX axis is equal to:
S = vt = x – x 0
where x 0 is the initial coordinate of the body, x is the final coordinate of the body (or the coordinate of the body at any time)
Equation of motion, that is, the dependence of the body coordinates on time x = x(t), takes the form:
X = x 0 + vt
If the positive direction of the OX axis is opposite to the direction of motion of the body, then the projection of the body’s velocity onto the OX axis is negative, the speed is less than zero (v< 0), и тогда уравнение движения принимает вид:
X = x 0 - vt
Dependence of speed, coordinates and path on time
The dependence of the projection of the body velocity on time is shown in Fig. 1.11. Since the speed is constant (v = const), the speed graph is a straight line parallel to the time axis Ot.
Rice. 1.11. Dependence of the projection of body velocity on time for uniform rectilinear motion.
The projection of movement onto the coordinate axis is numerically equal to the area of the rectangle OABC (Fig. 1.12), since the magnitude of the movement vector is equal to the product of the velocity vector and the time during which the movement was made.
Rice. 1.12. Dependence of the projection of body displacement on time for uniform rectilinear motion.
A graph of displacement versus time is shown in Fig. 1.13. The graph shows that the projection of the velocity is equal to
V = s 1 / t 1 = tan α
where α is the angle of inclination of the graph to the time axis. The greater the angle α, the faster the body moves, that is, the greater its speed (the greater the distance the body travels in less time). The tangent of the tangent to the graph of the coordinate versus time is equal to the speed:
Tg α = v
Rice. 1.13. Dependence of the projection of body displacement on time for uniform rectilinear motion.
The dependence of the coordinate on time is shown in Fig. 1.14. From the figure it is clear that
Tg α 1 > tg α 2
therefore, the speed of body 1 is higher than the speed of body 2 (v 1 > v 2).
Tg α 3 = v 3< 0
If the body is at rest, then the coordinate graph is a straight line parallel to the time axis, that is
X = x 0
Rice. 1.14. Dependence of body coordinates on time for uniform rectilinear motion.
This manual includes training tasks. tests for self-control, independent work, tests and examples of solving typical problems. The proposed didactic materials are compiled in full accordance with the structure and methodology of the textbook by A. V. Peryshkina, K. M. Gutnik “Physics. 9th grade."
TZ-1. Path and movement.
1. Indicate in which of the examples below the body can be considered a material point:
a) The Earth moving around the Sun;
b) The Earth rotating around its axis;
c) the Moon revolving around the Earth;
d) the Moon, on the surface of which the lunar rover moves;
e) a hammer thrown by an athlete;
e) a sports hammer, which is made on a machine.
2. What does a bus passenger determine by the numbers on the kilometer posts installed along the highway - the movement or the distance traveled by the bus?
3. Figure 1 shows the flight paths of projectiles. Are the distances traveled by the projectiles equal for these movements? moving?
4. A body thrown vertically upward from point A fell into the shaft (Fig. 2). What are the distance traveled by the body and the displacement module if AB = 15 m, BC - 18 m?
5. The athlete will have to run one lap (400 m). What is the displacement module equal to if he: a) ran 200 m of the path; b) finished? Consider the stadium track to be a circle.
6. The squirrel runs inside the wheel, being at the same height relative to the floor. Are the path and displacement equal for such a movement?
Preface.
TRAINING TASKS
TZ-1. Path and movement.
TZ-2. Rectilinear uniform motion.
TZ-3. Relativity of motion.
TZ-4. Rectilinear uniformly accelerated motion.
TZ-5. Newton's laws.
TZ-6. Free fall of bodies.
TZ-7. The law of universal gravitation. Body movement
TZ-8.Body impulse. Law of conservation of momentum.
Law of energy conservation.
TZ-9. Mechanical vibrations and waves. Sound.
TZ-10. Electromagnetic field.
TZ-11. The structure of the atom and the atomic nucleus.
SELF-CONTROL TESTS
TS-1. Rectilinear uniform motion.
TS-2. Rectilinear uniformly accelerated motion.
TS-3. Newton's laws.
TS-4. Free fall of bodies.
TS-5. The law of universal gravitation. Body movement
around the circumference. Artificial Earth satellites..
TS-6. Body impulse. Law of conservation of momentum.
Law of energy conservation.
TS-7. Mechanical vibrations.
TS-8. Mechanical waves. Sound.
TS-9. Electromagnetic field.
TS-10. The structure of the atom and the atomic nucleus.
INDEPENDENT WORK
SR-1. Path and movement.
SR-2. Rectilinear uniform motion.
SR-3. Rectilinear uniform motion.
Graphic tasks.
SR-4. Relativity of motion.
SR-5. Rectilinear uniformly accelerated motion..
SR-6. Rectilinear uniformly accelerated motion.
Graphic tasks.
SR-7. Newton's laws.
SR-8. Free fall of bodies.
SR-9. The law of universal gravitation.
Artificial Earth satellites.
SR-10. Movement of a body in a circle.
SR-11. Body impulse. Law of conservation of momentum.
Law of energy conservation.
SR-12. Mechanical vibrations.
SR-13. Mechanical waves. Sound.
SR-14. Electromagnetic field.
SR-15. The structure of the atom and the atomic nucleus.
TEST PAPERS
KR-1. Rectilinear uniformly accelerated motion.
KR-2. Newton's laws.
KR-3. The law of universal gravitation. Body movement
around the circumference. Artificial Earth satellites.
KR-4. Law of conservation of momentum.
Law of energy conservation.
KR-5. Mechanical vibrations and waves.
KR-6. Electromagnetic field.
EXAMPLES OF SOLVING TYPICAL PROBLEMS
Laws of interaction and movement of bodies.
Mechanical vibrations and waves.
Electromagnetic field.
ANSWERS
Training tasks.
Tests for self-control.
Independent work.
Test papers.
Bibliography.
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