Movement and reporting system

Содержание и основные понятия

The Kinematic describes the movement without identifying its causes, the position is given by coordinates and the movement by vector from the initial point to the end.
GEF · Grade 9
PIF · Baseline
Interactive model
Reporting system
coordinate
route
Movement
Projection
01
The physical picture
What happens and what boundaries the model has.
Main message
The Kinematic describes the movement without identifying its causes, the position is given by coordinates and the movement by vector from the initial point to the end.
The path depends on the shape of the trajectory, the movement depends only on the initial and final position.
The coordinate and speed depend on the selected system of the countdown.
The vector projection may be positive, negative or zero.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
Δ
x
=
x
−
x
0
\Delta x=x-x_0
Δ
x
=
x
−
x
0
​
displacement projection
v
⃗
ср
=
Δ
r
⃗
Δ
t
\vec v_{\mathrm{ср}}=\frac{\Delta\vec r}{\Delta t}
v
cf
​
=
Δ
t
Δ
r
​
average vector speed
Review of the situation
After a full circle around the stadium, the path is equal to the length of the track and the movement is zero.
04
Links and application
In the real world
After a full circle around the stadium, the path is equal to the length of the track and the movement is zero.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Transfer and reporting system" through the model, not just the formula.
Outcome 2
Clear and correctly use terms: counting system, coordinates, path.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Reporting system
The countdown body, the related coordinate system and the time measurement method.
coordinate
The number that sets the point position relative to the selected beginning and axis of the coordinates.
route
A scalar value equal to the length of the trajectory section.
Movement
A vector that connects the body's initial position to the end.
Projection
Algebraic scalar component of the vector on the chosen axle.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
Δ
x
=
x
−
x
0
\Delta x=x-x_0
Δ
x
=
x
−
x
0
​
definition
The projection of displacement.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
x
0
=
x
(
t
0
)
,
x
=
x
(
t
)
x_0=x(t_0),\quad x=x(t)
x
0
​
=
x
(
t
0
​
)
,
x
=
x
(
t
)
The axis shall be fixed and the initial and final coordinates of the body in the selected system of countdown shall be noted.
Δ
x
≡
x
кон
−
x
нач
\Delta x\equiv x_{\text{кон}}-x_{\text{нач}}
Δ
x
≡
x
Cot
​
−
x
start
​
The displacement projection is defined as a change of coordinates, not taken out of another law.
Δ
x
=
x
−
x
0
\Delta x=x-x_0
Δ
x
=
x
−
x
0
​
The installation of the final and initial coordinates gives the recorded formula; the sign shows the direction of movement relative to the axis.
Conditions:
Traffic is considered along the chosen axle; x and x_0 are measured in the same reporting system and in one unit.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
v
⃗
ср
=
Δ
r
⃗
Δ
t
\vec v_{\mathrm{ср}}=\frac{\Delta\vec r}{\Delta t}
v
cf
​
=
Δ
t
Δ
r
​
definition
Average vector speed.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
r
⃗
=
r
⃗
2
−
r
⃗
1
,
Δ
t
=
t
2
−
t
1
\Delta\vec r=\vec r_2-\vec r_1,\quad \Delta t=t_2-t_1
Δ
r
=
r
2
​
−
r
1
​
,
Δ
t
=
t
2
​
−
t
1
​
For the chosen interval, the displacement vector and its duration are found.
v
⃗
ср
≡
перемещение
время
\vec v_{\mathrm{ср}}\equiv\frac{\text{перемещение}}{\text{время}}
v
cf
​
≡
time
Movement
​
The average vector speed is defined as the ratio of movement to time, so its direction coincides with the direction of displacement.
v
⃗
ср
=
Δ
r
⃗
Δ
t
\vec v_{\mathrm{ср}}=\frac{\Delta\vec r}{\Delta t}
v
cf
​
=
Δ
t
Δ
r
​
Unlike the average travel speed, the numerator does not have a track length, but a vector between the initial and the final positions.
Conditions:
Applicable to any final interval at Δt>0; both coordinates are specified in the same reporting system.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this topic is that the path depends on the shape of the trajectory, the movement depends only on the initial and final position.
How to Check the Mind
The coordinate and the speed depend on the selected system. Then check the units, vector direction, and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Movement and reporting system
The Kinematic describes the movement without identifying its causes, the position is given by coordinates and the movement by vector from the initial point to the end.
The path depends on the shape of the trajectory, the movement depends only on the initial and final position.
The coordinate and speed depend on the selected system of the countdown.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.