Topicm021a3b4b623cc023_1528449000663_0Topic

VelocityvelocityVelocity and its units. Reading speed and distancedistancedistance from graphs

Levelm021a3b4b623cc023_1528449084556_0Level

Second

Core curriculumm021a3b4b623cc023_1528449076687_0Core curriculum

II. Solving problems using physical laws and relationships. Student:

3) converts time units (seconds, minutes, hours);

4) uses the concept of velocity to describe the rectilinear motion; calculates its magnitude (speed) and converts its units.

Timingm021a3b4b623cc023_1528449068082_0Timing

45 minutes

General learning objectivesm021a3b4b623cc023_1528449523725_0General learning objectives

Reading speed and distance values from graphs.

Key competencesm021a3b4b623cc023_1528449552113_0Key competences

1. Calculation of speed.

2. Reading values of quantities describing motion based on graphs.

Operational (detailed) goalsm021a3b4b623cc023_1528450430307_0Operational (detailed) goals

The student:

- calculates speed,

- reads from the graphs values of quantities describing motion of bodies.

Methodsm021a3b4b623cc023_1528449534267_0Methods

1. Learning by observation.

2. Learning by applying the known rules and solving problem tasks.

Forms of workm021a3b4b623cc023_1528449514617_0Forms of work

1. Individual cooperation between the student and the teacher.

2. Work with the whole class.

Lesson stages

Introductionm021a3b4b623cc023_1528450127855_0Introduction

Task 1

List the quantities describing motion of the body.

Answer:
The quantities describing motion of the body include: velocityvelocityvelocity, distance and time.

Task 2

How can one unambiguously determine if the body is in motion or at rest?

Answer:
For unambiguous determination of the body motion, one should choose the reference frame related to which we will consider the body motion.

Task 3

List the basic units of length and time in the SI system.

Answer:
The unit of length is meter [m], and of time is second [s].

Procedurem021a3b4b623cc023_1528446435040_0Procedure

Task 4

You can use the following requisites: stopwatch, ruler, battery car.

Suggest a way to determine the speed of this car.

Answer:

1. I mark two sections of the length $s_1=1m$ and $s_2=2m$.
2. I measure the time on each of the sections, e.g.  $t_1=0,82s$ and $t_2=1,66s$.
3. I describe the speed of car substitute to the formula:

Summary:

The value obtained as a result of the mathematical calculations is the average value of speed, the so‑called average speed.m021a3b4b623cc023_1527752256679_0The value obtained as a result of the mathematical calculations is the average value of speed, the so‑called average speed.

where:
$s\left[m\right]$ - distancedistancedistance travelled in meters,
$t\left[s\right]$ - time of travel in seconds,
$v_{av}\left[\frac{m}{s}\right]$ - average speed in meters per second.

Different values of the speed of moving bodies.

[Interactive graphics]

Task 5

Look at the photo of the speedometer and answer the questions.

[Illustration 1]

1. Read the speed of the car.
2. Is it the average speed?

Answer:

1. The speed is 190 $\frac{{\displaystyle km}}{h}$.
2. It is not the average speed, it is the speed of the car at a given instant in time, i.e. the instantaneous speed.

Definition:

The speed of the body at a given instant in time is the instantaneous speed.

Task 6

The figure shows two cars moving on the same track in two different directions. The instantaneous velocity of the first has a value $v_1=70\frac{km}{h}$ and the second $v_2=80\frac{km}{h}$.
Present these two velocities graphically. Think about what physical quantity (scalar, vector) is velocity.

[Illustration 2]

Answer:

[Illustration 3]

VelocityvelocityVelocity is a vector quantity because it has a magnitude (speed) and direction (return or sense).

Task 7

Convert the speed of 54 $\frac{{\displaystyle km}}{h}$ to $\frac{{\displaystyle m}}{s}$.

Answer.

$1km=1000mand1h=3600s$

$54\frac{km}{h}=54\cdot \frac{1000m}{3600s}=\frac{540m}{36s}=15\frac{m}{s}$

Task 8

Convert the speed of 20 $\frac{{\displaystyle m}}{s}$ to $\frac{{\displaystyle km}}{h}$.

Answer.

$20\frac{m}{s}=20\cdot \frac{1}{1000}km÷\frac{1}{3600}h=20\cdot \frac{36km}{10h}=72\frac{km}{h}$

Task 9

Choose the right answers.

The students converted the cyclist's speed of 5,5 $\frac{{\displaystyle m}}{s}$ to other speed units. Which values represent the correct conversion:

a) 19,8 $\frac{{\displaystyle km}}{h}$

b) 550 $\frac{{\displaystyle \mathrm{cm}}}{\min }$

c) 33000 $\frac{{\displaystyle \mathrm{cm}}}{\min }$

d) 198000 $\frac{{\displaystyle m}}{h}$

e) 19800 $\frac{{\displaystyle m}}{h}$

Answer:

a) True. b) False. c) True. d) False. e) True.

Task 10

Physical quantities describing physical phenomena or processes can be presented graphically. By presenting the quantities describing the motion, we most often use the graphs illustrating the dependence of the speed on time v(t) and the distancedistancedistance on time s(t).

Using the table below:

a) make a distance‑time graphgraphgraph,

b) make a speed‑time graph for this motion.

[Table 1]

Answer:

[Illustration 4]

Task 11

Using the distancedistancedistance vs. time graphgraphgraph shown in illustration, select the correct answers to the given sentences.

[Illustration 5]

1. The body travelled within 8 seconds:

a) 30 m
b) 20 m
c) 40 m

2. The first 20 m the body travelled in:

a) 4 s
b) 5 s
c) 2 s

3. The speed of this body was:

a) 10 $\frac{{\displaystyle m}}{s}$
b) 20 $\frac{{\displaystyle m}}{s}$
c) 5 $\frac{{\displaystyle m}}{s}$

Answer:

1 - c
2 - a
3 - c

Task 12

Using the speed vs. time graph, select the correct answers to the given sentences.

[Illustration 6]

1. The average speed of this body is:

a.) 20 $\frac{{\displaystyle m}}{s}$
b) 25 $\frac{{\displaystyle m}}{s}$
c) 30 $\frac{{\displaystyle m}}{s}$

2. After 30 seconds, the body moved with speed:

a) 30 $\frac{{\displaystyle m}}{s}$
b) 20 $\frac{{\displaystyle m}}{s}$
c) you cannot state, no data.

3. The distance travelled by the body after 10 seconds was:

a) 3 m
b) 300 m
c) 30 m

Answer:

1 - c
2 - c
3 - b

Lesson summarym021a3b4b623cc023_1528450119332_0Lesson summary

1. If the distance travelled by the body is divided by the time of travel, we calculate the average speed. The average speed is calculated using the formula:

where:
$s\left[m\right]$ - distancedistancedistance travelled in meters,
$t\left[s\right]$ - time of travel in seconds,
$v_{av}\left[\frac{m}{s}\right]$ - average speed value.

2. The instantaneous speed is the speed of the body at a given instant in time (in a very short time interval). If we measure speed in a long time interval, then the average speed usually differs significantly from instantaneous speed. When the time interval is very small (approaches zero), the average speed approaches the instantaneous speed.

3. To graphically represent the relationships between physical quantities describing phenomena or processes, we use graphs. We name the distance vs. time graphgraphgraph - as s(t), and the speed vs. time graph - as v(t).

Selected words and expressions used in the lesson plan

average velocityaverage velocityaverage velocity

distancedistancedistance

graphgraphgraph

instantaneous velocityinstantaneous velocityinstantaneous velocity

velocityvelocityvelocity