Topicm1681ff3f718b4838_1528449000663_0Topic

Summary of kinematicskinematicskinematics

Levelm1681ff3f718b4838_1528449084556_0Level

Second

Core curriculumm1681ff3f718b4838_1528449076687_0Core curriculum

I. The use of physical concepts and quantities to describe phenomena and to indicate their examples in the surrounding reality.

II. The student:

1) extracts from the texts, tables, diagrams or graphs, schematic or block drawings, key information for the described phenomenon or problem; illustrates them in various forms;

2) extracts the phenomenon from its context, names it and indicates factors that are important and irrelevant to its occurence.

Timingm1681ff3f718b4838_1528449068082_0Timing

45 minutes

General learning objectivesm1681ff3f718b4838_1528449523725_0General learning objectives

Consolidation of knowledge concerning kinematicskinematicskinematics.

Key competencesm1681ff3f718b4838_1528449552113_0Key competences

1. Recognition of the quantities describing the motion and their presentation on the graphs.

2. Determining types of motion based on the distance travelled and the speed change.

Operational (detailed) goalsm1681ff3f718b4838_1528450430307_0Operational (detailed) goals

The student:

- recognizes and classifies types of motion,

- describes motion verbally, using mathematical formulas or graphically.

Methodsm1681ff3f718b4838_1528449534267_0Methods

1. Learning by observation.

2. Teaching by applying appropriate laws and solving problem tasks.

Forms of workm1681ff3f718b4838_1528449514617_0Forms of work

1. Cooperation between the student and the teacher.

2. Work with the whole class to solve tasks.

Lesson stages

Introductionm1681ff3f718b4838_1528450127855_0Introduction

Prepare answers for the following questions or complete tasks:

1. What is motion and what is its relativity of motion?
2. What is trajectorytrajectorytrajectory of motion?
3. What is the distance?
4. What is the displacement?
5. Define the concept of velocity.
6. What motion is called a uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion?
7. Draw a graph of speed vs. time in uniform rectilinear motion.
8. What motion is called uniformly accelerated motion?
9. Draw a graph of speed vs. time in uniformly accelerated motion.
10. What is acceleration?
11. Draw a graph of distance vs. time in uniformly accelerated motion.
12. What is non‑uniformly variable motion?
13. Explain the concept of instantaneous and average velocity.

Procedurem1681ff3f718b4838_1528446435040_0Procedure

1. What is motion and what is its relativity of motion?

Motion is the change in the position of the body relative to a reference frame. To determine whether the body is in motion or at rest, we must first select the reference frame and determine the position of the body relative to it. Typically, the reference frame is the surface of the Earth and the body that are rigidly connected to it (trees, houses, etc.) The same body can be moving relative to one reference frame, and at the same time be at rest relative to another. Such a feature is called relativity of motion.m1681ff3f718b4838_1527752256679_0Motion is the change in the position of the body relative to a reference frame. To determine whether the body is in motion or at rest, we must first select the reference frame and determine the position of the body relative to it. Typically, the reference frame is the surface of the Earth and the body that are rigidly connected to it (trees, houses, etc.) The same body can be moving relative to one reference frame, and at the same time be at rest relative to another. Such a feature is called relativity of motion.

2. What is trajectory of motion?

TrajectorytrajectoryTrajectory of motion is the line along which the body moves. Due to the shape of the trajectory, the motion is divided into a rectilinear and curvilinear.

3. What is distance?

The length of the trajectory is called distance.

4. What is the displacement?

The vector connecting the initial position of the body with its final position is called displacement.

5. Define the concept of velocity.

Velocity is the quotient of the displacement and time of this displacement.

In rectilinear motion, the magnitude of displacement is equal to the distance, so the magnitude of velocity (speed) can also be calculated as the quotient of the distance to the time:

Velocity is a vector quantity. In rectilinear motion the direction of velocity is the same as the direction of displacement. The basic velocity unit in the SI system is 1 $\frac{m}{s}$.

6. What motion is called a uniform rectilinear motion?

Uniform rectilinear motionuniform rectilinear motionUniform rectilinear motion is a motion which trajectorytrajectorytrajectory is a straight line and the speed has a constant value.

7. Draw a graph of speed vs. time in uniform rectilinear motion.

The dependence of speed on time in uniform motion can be presented in the graph:

[Illustration 1]

The distance in uniform motion is directly proportional to time.

The dependence of the distance on time in uniform motion is shown in the graph:

[Illustration 2]

8. What motion is called uniformly accelerated motion?

Uniformly accelerated motion is a motion in which the speed in every second increases by the same amount.

9. Draw a graph of speed vs. time in uniformly accelerated motion.

Speed in this motion is directly proportional to time. This dependence can be presented in the graph:

[Illustration 3]

10. What is acceleration?

The quotient of the velocity change to the time when this change occurred is called acceleration.

Acceleration is a vector quantity. The direction of the acceleration in the rectilinear motion is the same as the direction of the velocity change. The unit of acceleration is 1 $\frac{{\displaystyle m}}{s^2}$.

11. Draw a graph of distance vs. time in uniformly accelerated motion.

In uniformly accelerated motion, the acceleration is constant. In a uniformly accelerated motion, the distance is directly proportional to the square of time. It can be calculated using the formula (when the initial speed is 0):

The dependence of the distance on time can be presented on the graph:

[Illustration 4]

The distance differences covered in the consecutive seconds in uniformly accelerated motion are related to each other like the consecutive odd numbers.

12. What is non‑uniformly variable motion?

Most often we are dealing with a non‑uniform motion.

Non‑uniform motion (variable) is a motion during which the speed changes. A car that covered 60 km in 1 hour certainly did not move at a speed of 60 $\frac{km}{h}$ all the time. There were moments when it accelerated, it slowed down and moments when it moved in uniform motion. It could even stop for a moment.

13. Explain the concept of instantaneous and average velocity.

The quotient of the total distance and time in which it was covered is called the average speed.

The velocity of the body at a given instant (instantaneous velocity) is the quotient of the displacement to the very small time interval Δt in which it occurred.

From the speed vs. time graph, you can read the distance the body covered as an area under the graph (regardless of the type of motion).

[Interactive graphics]

Task 1

The table below contains data on the motion of two cars moving in rectilinear motion, one of them moving in a uniformly accelerated motion. Based on that, complete the table, make graphs of speed vs. time. Give the name of the motion that the cars were moving. Calculate the acceleration for these motions. The initial speed is 0.

[Table 1]

Answer:

[Table 2]

The motion of the car 1 is uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion with the speed $v_1=2\frac{{\displaystyle m}}{s}$.

The motion of the car 2 is uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion with acceleration $a_2=2\frac{{\displaystyle m}}{s}$.

$s=\frac{a\cdot t^2}{2}$

hence:

$a_2=\frac{{\displaystyle 2·s}}{t^2}$

$a_2=2\frac{{\displaystyle m}}{s^2}$

[Illustration 5]

Task 2

Marek travelled the first section at a speed of 50 $\frac{km}{h}$ in 30 min, and the second during 1,5 h at a speed of 20 $\frac{m}{s}$. Calculate the average speed on the travelled distance.

Analysis:

Given:

$v_1=50\frac{{\displaystyle km}}{h}$

$v_2=20\frac{{\displaystyle m}}{s}=72\frac{{\displaystyle km}}{h}$

$t_1=30min=\frac{{\displaystyle 1}}{2}h$

$t_2=1,5h$

Unknown:

$v_{av}=?$

Solution:

$v_{av}=\frac{{\displaystyle s_1+s_2}}{t_1+t_2}$

$s_1=v_1·t_1$

$s_2=v_2·t_2$

$s_1=50\frac{{\displaystyle km}}{h}·\frac{{\displaystyle 1}}{2}h$

$s_1=25km$

$s_2=72\frac{km}{h}\cdot 1\frac{1}{2}h$

$s_2=108km$

$v_{av}=\frac{25km+108km}{0,5h+1,5h}$

$v_{av}=\frac{133km}{2h}$

$v_{av}=66,5\frac{km}{h}$

Answer:

Average speed was 66,5 $\frac{km}{h}$.

Task 3

The tram moved at 21,6 $\frac{km}{h}$ and braked in 6 seconds. Determine the braking distance and the decelerationdecelerationdeceleration of the tram.

Analysis:

Given:

$v=21,6\frac{{\displaystyle km}}{h}=6\frac{{\displaystyle m}}{s}$

$t=6s$

$v_f=0$

Unknown:

$s=?$

$a=?$

Solution:

$a=\frac{{\displaystyle v}}{t}$

$a=\frac{{\displaystyle 6\frac{{\displaystyle m}}{s}}}{6s}$

$a=1\frac{{\displaystyle m}}{s^2}$

$s=\frac{{\displaystyle a·t^2}}{2}$

$s=\frac{{\displaystyle 1\frac{{\displaystyle m}}{s^2}}}{2}·{\left(6s\right)}^2$

$s=18m$

Answer:

Distance covered by the tram is 18 m and decelerationdecelerationdeceleration is 1 $\frac{{\displaystyle m}}{s^2}$.

Task 4

The graph shows the dependence of speed of the body on time. Specify the type of body motion in individual sections. Calculate the value of the distance the body has travelled in this motion.

[Illustration 6]

Answer:

Section I - decelerated motion; s = 30 m,
Section II - the body is at rest s = 0,
Section III - accelerated motion s = 20 m.

Total distance 50 m

Lesson summarym1681ff3f718b4838_1528450119332_0Lesson summary

Kinematics deals with the description of motion. We use the concept of a reference frame to describe motion. To describe motion, it is necessary to introduce the trajectory. Among rectilinear motions, we distinguish uniform rectilinear motion, uniformly accelerated rectilinear motion, uniformly decelerated rectilinear motion. A complex motion is a motion in which one can distinguish corresponding known types of motion - uniform rectilinear, uniformly accelerated or uniformly decelerated.m1681ff3f718b4838_1527752263647_0Kinematics deals with the description of motion. We use the concept of a reference frame to describe motion. To describe motion, it is necessary to introduce the trajectory. Among rectilinear motions, we distinguish uniform rectilinear motion, uniformly accelerated rectilinear motion, uniformly decelerated rectilinear motion. A complex motion is a motion in which one can distinguish corresponding known types of motion - uniform rectilinear, uniformly accelerated or uniformly decelerated.

Selected words and expressions used in the lesson plan

complex motioncomplex motioncomplex motion

decelerationdecelerationdeceleration

kinematicskinematicskinematics

trajectorytrajectorytrajectory

uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

uniformly decelerated rectilinear motionuniformly decelerated rectilinear motionuniformly decelerated rectilinear motion