Topicm2f8207370572fcf0_1528449000663_0Topic

Drawing and analysing graphs of distancedistancedistance and velocityvelocityvelocity dependence on time in uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion

Levelm2f8207370572fcf0_1528449084556_0Level

Second

Core curriculumm2f8207370572fcf0_1528449076687_0Core curriculum

II. Solving problems using physical laws and relationships. The student:

6) determines the value of speed and distance from the graphs of the speed and distance vs. time for rectilinear motion with uniform sections and draws these graphs based on the given information.

Timingm2f8207370572fcf0_1528449068082_0Timing

45 minutes

General learning objectivesm2f8207370572fcf0_1528449523725_0General learning objectives

Drawing graphs describing uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion.

Key competencesm2f8207370572fcf0_1528449552113_0Key competences

1. Drawing graphs $s\left(t\right)$ and $v\left(t\right)$.

2. Reading quantities describing uniform linear motion from graphs.

Operational (detailed) goalsm2f8207370572fcf0_1528450430307_0Operational (detailed) goals

The student:

- draws graphs $s\left(t\right)$ and $v\left(t\right)$ in uniform rectilinear motion,

- reads quantities describing uniform linear motion from graphs.

Methodsm2f8207370572fcf0_1528449534267_0Methods

1. Discussion.

2. Solving problem tasks.

Forms of workm2f8207370572fcf0_1528449514617_0Forms of work

1. Cooperation between the student and the teacher.

2. Individual work.

Lesson stages

Introductionm2f8207370572fcf0_1528450127855_0Introduction

Task 1

Answer the questions:

1. List the characteristics of uniform rectilinear motion.
2. Give the formula for speed in this motion.
3. Draw the graphgraphgraph $s\left(t\right)$ and $v\left(t\right)$ describing this motion.

Answer:

1. Uniform rectilinear motion is a motion where the trajectory is a straight line and the speed does not change.
2. The speed in uniform rectilinear motion is determined from the formula:

3. [Illustration 1]

Procedurem2f8207370572fcf0_1528446435040_0Procedure

Task 2

The table contains distancedistancedistance-time dependence for a motion of a body. Complete the given table. Give the name of the motion of this body. Calculate the speed of the body. Make graphs $s\left(t\right)$ and $v\left(t\right)$ for the motion of this body.

[Table 1]

Answer:

It is a uniform motionuniform motionuniform motion. The speed in this motion is $v=\frac{s}{t}$, $v=2\frac{m}{s}$.

[Illustation 2]

[Interactive graphics]

Familiarize yourself with an interactive drawing showing a graph of the dependency of distance on time for a body moving in a straight line, with sections of different speed.

Task 3

The graph shows the dependency of distance on time for a certain vehicle:

[Illustration 3]

Based on the graph:

1. What is the type of motion of the vehicle in each sectionsectionsection?
2. Calculate the vehicle speed in these sections.
3. In which section the body has the highest speed?
4. What is the average speed over the entire distancedistancedistance?

Answer:

1.

- section A - uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion,
- section B - uniform rectilinear motion,
- section C - the body is at rest.

2.

- section A

$v=\frac{s}{t}$

$v=\frac{12m}{6s}$

- section B

$v=\frac{s_2-s_1}{t_2-t_1}$

$v=\frac{16m-12m}{12s-6s}$

$v=\frac{4m}{6s}$

$v=\frac{2}{3}\frac{m}{s}$

- section C - $v=0$ the body is at rest.

3.

The body has the highest speed in sectionsectionsection A.

4.

$v=\frac{s}{t}$

$v=\frac{16m}{18s}$

$v=\frac{8}{9}\frac{m}{s}$

Based on the analysis of the $v\left(t\right)$graphgraphgraph of the body motion, we can determine the distance travelled after time t with the speed v:

[Illustration 4]

After analysing the graph $v\left(t\right)$ we can conclude that to calculate the distance, the area of the rectangle formed under the graph should be calculated.

In the graph $v\left(t\right)$ the area under the graph corresponds to the distance travelled by the moving body.

Task 4

The body was moving in uniform recti linear motion. The diagram $v\left(t\right)$ below shows the three sections of this motion; at these sections the speed of the body is constant. Draw a graph of distance vs. time for the motion of this body. Take the right scale in the time, distance and speed axes.m2f8207370572fcf0_1527752263647_0The body was moving in uniform recti linear motion. The diagram $v\left(t\right)$ below shows the three sections of this motion; at these sections the speed of the body is constant. Draw a graph of distance vs. time for the motion of this body. Take the right scale in the time, distance and speed axes.

[Illustration 5]

Answer:

[Illustration 6]

Task 5

Illustration shows the graph of $s\left(t\right)$:

[Illustration 7]

The graph above shows that the body speed is:

a) 200 $\frac{m}{s}$,
b) 20 $\frac{m}{s}$,
c) 80 $\frac{m}{s}$,
d) 8 $\frac{m}{s}$.

Answer:

d.

Task 6

The graphs show the relationship of distance to time for the movement of two bodies moving at different speeds.

[Illustration 8]

Which body moves with higher speed. Explain your answer.

Answer:

Body A has a higher speed because the angle of the graphgraphgraph with respect to the time axis (slopeslopeslope) is larger. This means that at the same time body A will cover a greater distance than body B.

Lesson summarym2f8207370572fcf0_1528450119332_0Lesson summary

1. The uniform rectilinear motion is presented graphically by means of graphs of the dependence of distance on time $s\left(t\right)$ and velocity on time $v\left(t\right)$.
2. The larger the slope of the graph $s\left(t\right)$ with respect to the time axis, the higher the speed at which the body moves.
3. If in the analysed time interval, the graph $s\left(t\right)$ is a horizontal line, then the corresponding graph $v\left(t\right)$ will be a straight line lying on the time axis.
4. In order to determine the distance from the graph $v\left(t\right)$ for the selected time interval, calculate the area of the rectangle formed under the graph $v\left(t\right)$.m2f8207370572fcf0_1527752256679_01. The uniform rectilinear motion is presented graphically by means of graphs of the dependence of distance on time $s\left(t\right)$ and velocity on time $v\left(t\right)$.
2. The larger the slope of the graph $s\left(t\right)$ with respect to the time axis, the higher the speed at which the body moves.
3. If in the analysed time interval, the graph $s\left(t\right)$ is a horizontal line, then the corresponding graph $v\left(t\right)$ will be a straight line lying on the time axis.
4. In order to determine the distance from the graph $v\left(t\right)$ for the selected time interval, calculate the area of the rectangle formed under the graph $v\left(t\right)$.

Selected words and expressions used in the lesson plan

distancedistancedistance

graphgraphgraph

sectionsectionsection

slopeslopeslope

uniform motionuniform motionuniform motion

uniform rectilinear motionuniform rectilinear motionuniform rectilinear motion

velocityvelocityvelocity