Topicm1a5e2ac5fee1919e_1528449000663_0Topic

Drawing and analysing graphs of distancedistancedistance and velocityvelocityvelocity dependence of time in uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

Levelm1a5e2ac5fee1919e_1528449084556_0Level

Second

Core curriculumm1a5e2ac5fee1919e_1528449076687_0Core curriculum

II. Solving problems using physical laws and relationships.

9) The student determines the change of speed and the magnitude of accelerationaccelerationacceleration from the graphs of the speed vs. time for uniformly variable (accelerated or decelerated) rectilinear motion.

Timingm1a5e2ac5fee1919e_1528449068082_0Timing

45 minutes

General learning objectivesm1a5e2ac5fee1919e_1528449523725_0General learning objectives

Presentation of graphs describing uniformly accelerated rectilinear motion.

Key competencesm1a5e2ac5fee1919e_1528449552113_0Key competences

1. Reading data from graphs describing uniformly accelerated rectilinear motion.

2. Preparing graphs of s(t), v(t) and a(t) for uniformly accelerated rectilinear motion.

3. Calculation based on graphs of distance, acceleration and speed.

Operational (detailed) goalsm1a5e2ac5fee1919e_1528450430307_0Operational (detailed) goals

The student:

- draws graphs of s(t), v(t) and a(t) for uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion,

- calculates based on graphs distance, acceleration and speed.

Methodsm1a5e2ac5fee1919e_1528449534267_0Methods

1. Learning by solving problems.

2. Discussion developing in the course of common problem solving by a class or group.

Forms of workm1a5e2ac5fee1919e_1528449514617_0Forms of work

1. Individual work.

2. Talk.

Lesson stages

Introductionm1a5e2ac5fee1919e_1528450127855_0Introduction

Task 1

a) What quantities describe uniformly accelerated motion?

b) Present these quantities.

c) What graphs were there in uniformly rectilinear motion?

d) Draw the graphs of s(t) and v(t) in uniform rectilinear motion.

Answer:

a) Uniformly accelerated motion is described by a constant magnitude of accelerationaccelerationacceleration - a. The speed in this motion increases by the same amount at equal time intervals.

b) The final velocityvelocityvelocity, which the body, having the initial velocity $v_o=0$, reached in uniformly accelerated rectilinear motion, we can determine from the formula:

where:
$v_f\left[\frac{m}{s}\right]$ - final speed of the body,
$a\left[\frac{m}{s^2}\right]$ - the acceleration of the body is constant,
Δt - the time interval in which the body moved with the specified accelerationaccelerationacceleration

c) In uniform rectilinear motion to analyse the movement were used distance vs. time graphs and speed vs. time graphs.

[Interactive illustration]

Procedurem1a5e2ac5fee1919e_1528446435040_0Procedure

Task 2

1. What quantity is constant in uniform rectilinear motion, and what in uniformly accelerated motion?
2. Draw a graphgraphgraph of a(t) in motion with constant acceleration.

In the uniformly accelerated rectilinear motion, the acceleration magnitude is constant. In the uniform rectilinear motion the velocity magnitude is constant and the acceleration magnitude is constant and equals 0.

[Illustration 1]

The graph of the acceleration value vs. time is a straight line parallel to the time axis. It illustrates that in uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion, acceleration is constant.

Task 3

1. How does the distance change depending on the time in uniform rectilinear motion? And how does the speed change in uniformly accelerated motion?
2. Draw a graph of v(t) in uniformly accelerated motion.m1a5e2ac5fee1919e_1527752263647_01. How does the distance change depending on the time in uniform rectilinear motion? And how does the speed change in uniformly accelerated motion?
2. Draw a graph of v(t) in uniformly accelerated motion.

Answers:

In a uniformly rectilinear motion, the distance traveled is proportional to the time and in the uniformly accelerated rectilinear the speed value changes in direct proportion to the time.

[Illustration 2]

Task 4

Draw a graphgraphgraph of speed vs. time if the initial speed is different from zero in the case of uniformly accelerated motion.

[Illustration 3]

Conclusions:

- In the uniformly accelerated value motion, the speed of the body in the same time intervals increases, and so the subsequent distances covered by this body must also increase.
- The graph of distance vs. time in uniformly accelerated rectilinear motion without initial speed is no longer a straight line.
- The curve that makes this graph is a part of a parabola, i.e. a graph of the quadratic function $y=a\cdot x^2$.

[Illustration 4]

The distancedistancedistance in uniformly accelerated motion is a quadratic function of time. We can present it using the formula:

[Slideshow]

Task 5

The graphgraphgraph shows the dependence of speed on time in uniformly accelerated motion. What is the distance travelled by the body after 4 seconds?

[Illustration 5]

a) 80 m
b) 5 m
c) 40 m
d) 20 m

Answer:

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

Lesson summarym1a5e2ac5fee1919e_1528450119332_0Lesson summary

- The graph of accelerationaccelerationacceleration vs. time is a straight line parallel to the time axis. This is because in uniformly accelerated motion the acceleration is constant.

- The area of the surface below the graph of speed vs. time in uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion is equal to the distance that the body travelled at a given time.

- If the body before the start of motion was in the rest state ($v_0=0$) and moves in a uniformly accelerated rectilinear motion, the distance is calculated using the formula:

where:
s [m] - distancedistancedistance,
a [$\frac{m}{s^2}$] - acceleration,
t [s] - time of motion.

- In uniformly accelerated rectilinear motion, the increase of the travelled distance in the subsequent seconds of motion are related to each other as the consecutive odd numbers.

Selected words and expressions used in the lesson plan

accelerationaccelerationacceleration

area under graph of speed vs. timearea under graph of speed vs. timearea under graph of speed vs. timearea under graph of speed vs. timearea under graph of speed vs. time

distancedistancedistance

graphgraphgraph

uniformly accelerated rectilinear motionuniformly accelerated rectilinear motionuniformly accelerated rectilinear motion

velocityvelocityvelocity