Topicmc76f427e2ce3b18e_1528449000663_0Topic

Uniform rectilinear motionuniform rectilinear motionUniform rectilinear motion and uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion in tasks

Levelmc76f427e2ce3b18e_1528449084556_0Level

Second

Core curriculummc76f427e2ce3b18e_1528449076687_0Core curriculum

II. Solving problems using physical laws and relationships.

6) The student performs calculations and writes down the result in accordance with the rules of rounding and keeping the number of significant digits resulting from the accuracy of the measurement or from the data.

Timingmc76f427e2ce3b18e_1528449068082_0Timing

45 minutes

General learning objectivesmc76f427e2ce3b18e_1528449523725_0General learning objectives

Solving problem problem task tasks.

Key competencesmc76f427e2ce3b18e_1528449552113_0Key competences

1. Analyzes the problem task.

2. Uses physical dependencies to solve accounting problems.

3. Reads and draws the graphs of the dependence of traffic parameters on time.

Operational (detailed) goalsmc76f427e2ce3b18e_1528450430307_0Operational (detailed) goals

The student:

- presents the problem solving notation,

- determines from the basic formulas the unknown quantities.

Methodsmc76f427e2ce3b18e_1528449534267_0Methods

1. Talk, brainstorming.

2. Learning by solving problem tasks.

Forms of workmc76f427e2ce3b18e_1528449514617_0Forms of work

1. Individual work.

2. Work with the whole class.

Lesson stages

Introductionmc76f427e2ce3b18e_1528450127855_0Introduction

Task 1

a) Provide a definition of uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion.
b) Give the definition of uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion.
c) How would you describe the concept of complex motioncomplex motioncomplex motion?

Answer:

a) Uniform rectilinear motion means that the body is moving at a constant speed along a trajectory that is a straight line. In the uniform rectilinear motion, the body travels the same distances at regular intervals.
b) Uniformly accelerated rectilinear motion means that the body moves with constant acceleration along the trajectory being a straight line. In uniformly accelerated rectilinear motion, the body speed increases by the same amount at regular intervals.
c) Complex motion is a motion in which phases representing known types of uniform motion and uniformly accelerated motion can be distinguished.mc76f427e2ce3b18e_1527752263647_0a) Uniform rectilinear motion means that the body is moving at a constant speed along a trajectory that is a straight line. In the uniform rectilinear motion, the body travels the same distances at regular intervals.
b) Uniformly accelerated rectilinear motion means that the body moves with constant acceleration along the trajectory being a straight line. In uniformly accelerated rectilinear motion, the body speed increases by the same amount at regular intervals.
c) Complex motion is a motion in which phases representing known types of uniform motion and uniformly accelerated motion can be distinguished.

Proceduremc76f427e2ce3b18e_1528446435040_0Procedure

Task 2

Which motion is shown in the graph below?

[Interactive graphics]

Task 3

The motorcyclist moved at a speed of 54 $\frac{{\displaystyle km}}{h}$ for 3 minutes and then increased his speed to 72 $\frac{{\displaystyle km}}{h}$ within 10 seconds. Calculate the acceleration and the total distancedistancedistance travelled by the motorcyclist. Draw a graph of speed vs. time for this motion.

Analysis:

Given:

$v_i=54\frac{km}{h}=15\frac{m}{s}$

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

$t_1=3min=180s$

$t_2=10s$

Unknown:

$a=?$

$s_c=?$

Solution:

$s_c=s_1+s_2$ (it is the sum of distances travelled in the uniform motion and the uniformly accelerated motion)

$s_1=v_i\cdot t_1$

$s_1=15\frac{m}{s}\cdot 180s$

$s_1=2700m$

Due to the fact that the initial speed in this part of the motion is not equal to 0, the formula for the distance has the form:

$s_2=v_i\cdot t_2+\frac{a\cdot t_2^2}{2}$

$a=\frac{v_f-v_i}{t_2}$

$a=\frac{20\frac{m}{s}-15\frac{m}{s}}{10s}$

$a=0,5\frac{m}{s^2}$

Hence:

$s_2=15\frac{m}{s}\cdot 10s+\frac{0,5\frac{m}{s^2}\cdot {\left(10s\right)}^2}{2}$

$s_2=150m+25m$

$s_2=175m$

$s_c=2700m+175m$

$s_c=2875m=2,875km$

Answer:

The acceleration of the motorcyclist is 0,5 $\frac{{\displaystyle m}}{s^2}$, covered distance is 2875 m or 2,875 km.

[Illustration 1]

Task 4

Based on the speed vs. time graph showing the complex motioncomplex motioncomplex motion.

a) determine what type of motion it is,

b) calculate the acceleration in individual sections,

c) calculate the distancedistancedistance travelled by the body.

[Illustration 2]

Answer:

a) Section I - uniform motion.
Section II - uniformly accelerated motion.

b) Section I - because it is uniform motion, the acceleration is 0.

$a=\frac{v_f-v_i}{t}$

$a=\frac{6\frac{m}{s}-6\frac{m}{s}}{4s}$

$a=0$

Section II

$a=\frac{v_f-v_i}{\Delta t}$

$a=\frac{8\frac{m}{s}-6\frac{m}{s}}{6s-4s}$

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

c) To calculate the distancedistancedistance travelled by the body, we calculate the surface area of the figure below the graph.

$s_c=s_1+s_2$

$s_1$ - area of the rectangle

$s_2$ - area of the trapezium

$s_1=v\cdot t$

$s_1=6\frac{m}{s}\cdot 4s$

$s_1=24m$

$s_2=\frac{(a+b)\cdot h}{2}$

$s_2=\frac{(6\frac{m}{s}+8\frac{m}{s})\cdot 2s}{2}$

$s_2=14m$

$s_c=24m+14m$

$s_c=38m$

Task 5

Using the information from the previous task, select which graph correctly shows the dependence of acceleration on time for this motion.mc76f427e2ce3b18e_1527752256679_0Using the information from the previous task, select which graph correctly shows the dependence of acceleration on time for this motion.

[Illustration 3]

Answer:

a) False. b) True. c) False.

Task 6

Draw a graph of the speed vs. time for the motion of a body moving along a straight line with an acceleration, which changes according to the graph below. The initial speed of the body was 0.

[Illustration 3]

Analysis:

1. We calculate the value of the final speedfinal speedfinal speed in the first section.

$a=\frac{∆v}{∆t}=\frac{v_f-v_i}{t}$

because, $v_i=0$, the formula takes the form $a=\frac{v_f}{t}$.

$v_f=a·t$

$v_f=4\frac{m}{s^2}\cdot 2s$

$v_f=8\frac{m}{s}$

The body after 2 s was moving in a uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion at the speed corresponding to the final speedfinal speedfinal speed in uniformly accelerated motion. The speed is 8 $\frac{{\displaystyle m}}{s}$.

[Illustration 4]

Lesson summarymc76f427e2ce3b18e_1528450119332_0Lesson summary

Graphs of acceleration vs. time and velocity vs. time allow for graphical representation of relationships between physical quantities describing non‑uniform and uniform rectilinear motions.

In any complex motioncomplex motioncomplex motion, you can distinguish between phases representing the type of motion we know.

Selected words and expressions used in the lesson plan

complex motioncomplex motioncomplex motion

distancedistancedistance

final speedfinal speedfinal speed

uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion