Topicm1093ef3d15def03b_1528449000663_0Topic

Studying uniformly decelerated rectilinear motionuniformly decelerated rectilinear motionuniformly decelerated rectilinear motion

Levelm1093ef3d15def03b_1528449084556_0Level

Second

Core curriculumm1093ef3d15def03b_1528449076687_0Core curriculum

II. Solving problems using physical laws and relationships.

7) The student names a uniformly accelerated motion – a motion in which the speed increases in unit time intervals by the same amount, and a uniformly decelerated motion - a motion in which the speed decreases in unit time intervals by the same amount.

Timingm1093ef3d15def03b_1528449068082_0Timing

45 minutes

General learning objectivesm1093ef3d15def03b_1528449523725_0General learning objectives

Defining uniformly decelerated motion.

Key competencesm1093ef3d15def03b_1528449552113_0Key competences

1. Recognition of characteristics of uniformly decelerated motion.

2. Recognition of graphs describing this motion.

3. Solving problem tasks.

Operational (detailed) goalsm1093ef3d15def03b_1528450430307_0Operational (detailed) goals

The student:

- recognizes characteristics of uniformly decelerated motion,

- recognizes the graphs describing this motion.

Methodsm1093ef3d15def03b_1528449534267_0Methods

1. Talk, discussion.

2. Formulating problems and ideas for solving them.

Forms of workm1093ef3d15def03b_1528449514617_0Forms of work

1. Individual work with a student.

2. Solving tasks, working with a textbook.

Lesson stages

Introductionm1093ef3d15def03b_1528450127855_0Introduction

Task 1

a) List the types of motion you know.
b) Give the definition of accelerationaccelerationacceleration.
c) List the physical quantities describing the known motions.
d) Provide a formula for acceleration and its unit.

Answer:

a) The known motions are divided into rectilinear and curvilinear due to the shape of the trajectory. Due to variable velocity - uniform rectilinear motion and non‑uniform motion. Among non‑uniform rectilinear motions, we distinguish uniformly accelerated rectilinear motion and uniformly decelerated rectilinear motion.
b) Acceleration describes the change of velocity per unit of time.
c) Known motions are characterized by the time of travel, distance, average velocity and instantaneous velocity as well as acceleration.
d) Acceleration is calculated using the formula:

The unit of acceleration in the SI system is $\frac{m}{s^2}$.

Procedurem1093ef3d15def03b_1528446435040_0Procedure

[Slideshow]

The following conclusions can be formulated based on the presented slides:

1. The car moves along a straight line.
2. The speed of the car decreases.
3. The initial speed value is 120 $\frac{km}{h}$ and the final speed is 0.
4. Using the formula, we can calculate its accelerationaccelerationacceleration.
5. The calculated acceleration has the value -3,33 $\frac{m}{s^2}$.

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

$v_f=0\frac{m}{s}$, then:

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

$a=\frac{-33,3\frac{m}{s}}{10s}=-3,33\frac{m}{s^2}$

6. The value opposite to the acceleration value is called the deley.
7. Motion in which the speed decreases in the same time by the same amount and the body moves in a straight line is called uniformly decelerated rectilinear motionuniformly decelerated rectilinear motionuniformly decelerated rectilinear motion.

Task 2

Using the drawn conclusions, draw a graph of acceleration (deceleration) vs. time and speed vs. time for this motion.m1093ef3d15def03b_1527752263647_0Using the drawn conclusions, draw a graph of acceleration (deceleration) vs. time and speed vs. time for this motion.

[Illustration 1]

A graph of distance vs. time in uniformly decelerated rectilinear motion without an initial speed is no longer a straight line. The curve that makes this graph is a part of the parabola.

[Illustration 2]

Task 3

The car reduces its speed from 72 $\frac{km}{h}$ to 54 $\frac{km}{h}$ in 15 seconds. Calculate the magnitude of acceleration and deceleration in this motion.

Analysis:

Given:

$v_i=72\frac{km}{h}$

$v_f=54\frac{km}{h}$

$t=15s$

Unknown:

$a=?$

$a_{\mathrm{o}}=?$

Solution:

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

$\Delta v=v_f-v_i$

$\Delta v=72\frac{km}{h}-54\frac{km}{h}$

$\Delta v=-18\frac{km}{h}=-5\frac{m}{s}$

$a=\frac{-5\frac{m}{s}}{15s}$

$a=-\frac{1}{3}\frac{m}{s^2}$

Answer:

Acceleration is $a=-\frac{1}{3}\frac{m}{s^2}$, it is negative, so deceleration in this motion is $a_0=-a=\frac{1}{3}\frac{m}{s^2}$, it is positive.

Task 4

Based on the acceleration vs. time graph, name the types of motion. Give time of motions.

[Illustration 3]

Answer:

Section I - uniformly accelerated motion, duration: 2 s.
Section II – uniform rectilinear motion, duration: 2 s.
Section III - uniformly decelerated motion, duration: 4 s.

Task 5

The bullet flying at a speed of 600 $\frac{{\displaystyle m}}{s}$ pushes into the embankment to a depth of 8 cm. Calculate the bullet deceleration.

Analysis:

Given:

$v_i=600\frac{m}{s}$

$s=8cm=0,08m$

$v_f=0\frac{m}{s}$

Unknown:

$a=?$

Solution:

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

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

$\Delta v=v_i-v_f$

$\Delta v=-v_i$

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

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

The acceleration vector in uniformly decelerated motion has the same direction and opposite sense to the velocity vector of the moving body. To the formula we substitute the acceleration as a positive value, and the fact that we are dealing with a uniformly decelerated motion is marked by inserting a minus in the right place. Therefore, the formula for the distance in uniformly decelerated motion takes the form:

$s=v_i\cdot \frac{v_i}{a}-\frac{a\cdot {\left(\frac{-v_i}{a}\right)}^2}{2}$

$s=\frac{v_i^2}{a}-\frac{v_i^2}{2a}=\frac{v_i^2}{2a}$

$a=\frac{v_i^2}{2s}[\frac{\frac{m^2}{s^2}}{m}=\frac{m^2}{s^2}\cdot \frac{1}{m}=\frac{m}{s^2}]$

$a=\frac{{600}^2}{2\cdot 0,08}$

$a=\frac{360000}{0,16}$

$a=2250000\frac{m}{s^2}$

Answer:

Deceleration is 2250000 $\frac{{\displaystyle m}}{s^2}$.

Task 6

Acceleration in uniformly decelerated motion:

a) has the same direction, and the same sense as velocity.
b) has a different direction than velocity.
c) has the same direction, and opposite sense to velocity.

Answer:

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

Lesson summarym1093ef3d15def03b_1528450119332_0Lesson summary

Uniformly decelerated rectilinear motion is a motion which trajectory is a straight line and the deceleration is constant.

The speed in this motion decreases over time.

The accelerationaccelerationacceleration in this motion is constant, with the same direction and opposite sense to the velocity.

Decelerated motion can be treated as an accelerated motion with negative acceleration. To avoid minus signs in the formulas, the quantity called decelerationdecelerationdeceleration with the value opposite to the acceleration value is introduced.

Selected words and expressions used in the lesson plan

accelerationaccelerationacceleration

brakingbrakingbraking

decelerationdecelerationdeceleration

reduction of velocityreduction of velocityreduction of velocity

stopstopstop

uniformly decelerated rectilinear motionuniformly decelerated rectilinear motionuniformly decelerated rectilinear motion