PHYSICS 1

PHYSICS 1: MECHANICS AND THERMODYNAMICS

PHYSICS 2: OSCILLATIONS, ELECTRICITY AND MAGNETISM

PHYSICS 3: WAVES, OPTICS AND MODERN PHYSICS

2

Introduction

1. Title: Physics 1

2. Credits: 3

3. Prerequisites:

Analytics analysis

4. Course Description

This course tends to give students opportunity to explore the basic

concepts, laws and application of Mechanics and Thermodynamics,

including:

Properties and laws of motion of particle, rigid body

Relationship among position, velocity and acceleration

Laws of linear momentum, angular momentum and energy

The kinetic theory of gases, thermodynamic quantities

Laws of Thermodynamics

3

Introduction

5. Textbook

1.

Raymond A. Serway and W. Jewett, Physics for Scientists and

Engineers with Modern Physics (9th Edition), Cengage

Learning, USA, 2014

2.

Trần Ngọc Hơi, Phạm Văn Thiều, Vật lý đại cương: Các

nguyên lý và ứng dụng, Tập 1: Cơ học và Nhiệt học, NXB Giáo

dục 2006

Reference Books

3.

Hugh D. Young and Roger A. Freedman, University Physics with

Modern Physics (13th Edition), Pearson Education, USA, 2012

4.

Paul A. Tipler and Gene Mosca, Physics for Scientists and

Engineers (6th Ed.), W. H. Freeman and Company, USA, 2008

5.

David Halliday, Cơ sở vật lý, tập 1, NXB Giáo dục, 2007

4

Introduction

6. Lesson plan

Week

1

2

3

4

Lesson

Preparation of student

Introduction

Chapter 1: Physics and measurement

Read the text book: 2-13

Chapter 2: Motion in one dimension

Read the text book: 21-47

Chapter 3: Montion in two dimensions

Read the text book: 78-98

Chapter 4: The laws of motion

Read the text book: 111-135

Solve problems of chapters 2, 3, 4

Prepare the solution of

problems by group

Chapter 5: Circular motion and other

applications of Newton’s laws

Read the text book: 150-167

Chapter 6: Energy of the system

Read the text book: 177-201

Chapter 7: Conservation of energy

Read the text book: 211-233

5

Introduction

6. Lesson plan

Week

5

6

7

8

Lesson

Preparation of student

Solve problems of chapters 5, 6, 7

Prepare the solution of

problems by group

Chapter 8: Linear momentum and

collisions

Read the text book: 247-279

Chapter 9: Rotation of rigid object about

a fiexd axis

Read the text book: 293-321

Solve problems of chapters 8, 9

Prepare the solution of

problems by group

Chapter 10: Angular momentum

Read the text book: 335-352

Chapter 11: Static equilibrium and

elasticity, Universal gravitation, Fluid

mechanics

Study by your self: 363-449

Introduction to the project of course

6

Introduction

6. Lesson plan

Week

Lesson

Preparation of student

Solve problems of chapters 10

Prepare the solution of

problems by group

Chapter 12: Tempurature and the first

law of Thermodynamics

Read the text book: 568-625

Chapter 13: The kinetic theory of gases

Read the text book: 626-652

10

Chapter 14: Heat engines, entropy and

the second law of Thermodynamics

Read the text book: 653-688

11

Solve problems of chapters 12, 13, 14

Prepare the solution of

problems by group

Represent the result of the project

Work in group to make the

product of the project and to

prepare a report of project

9

12

7

Introduction

7. Assessment Plan

Assessment Types

Assessment Components

Percentages

20%

A1. Learning activities

A1.1. Attendance

A1.2. Homework report

A1.3. Project

A2. Midterm Exam

A2.1. Written Test

20%

A3. Final Exam

A3.1. Written Test

60%

8. Student Responsibilities and Policies:

Attendance: It is compulsory that students attend at least 80%

of the course to be eligible for the final examination.

Missed tests: Students are not allowed to miss any of the tests.

There are very few exceptions

PART 1: MECHANICS

CHAPTER 1: PHYSICS AND MEASUREMENT

PHYSICS AND

MEASUREMENT

CHAPTER 1

PART 1: MECHANICS

9

CHAPTER 1: PHYSICS AND MEASUREMENT

Physics

Physics, the most fundamental physical science, is concerned with

the fundamental principles of the Universe.

The study of physics can be divided into six main areas:

Classical mechanics: concerning the motion of objects that are large

relative to atoms and move at speeds much slower than the speed of light

Relativity: a theory describing objects moving at any speed, even speeds

approaching the speed of light

Thermodynamics: dealing with heat, work, temperature, and the statistical

behavior of systems with large numbers of particles

Electromagnetism: concerning electricity, magnetism, and electromagnetic

fields

Optics: the study of the behavior of light and its interaction with materials

Quantum mechanics: a collection of theories connecting the behavior of

matter at the submicroscopic level to macroscopic observations

PART 1: MECHANICS

10

CHAPTER 1: PHYSICS AND MEASUREMENT

Physics and measurement

Like all other sciences, physics is based on experimental

observations and quantitative measurements.

Objectives: to identify fundamental laws governing natural

phenomena and use them to develop theories

Tool: Language of mathematics (a bridge between theory and

experiment)

Classical physics: includes the principles of classical mechanics,

thermodynamics, optics, and electromagnetism developed before

1900 (Newton mechanics)

Modern physics: a major revolution in physics began near the end

of the 19th century (theories of relativity and quantum mechanics)

PART 1: MECHANICS

11

CHAPTER 1: PHYSICS AND MEASUREMENT

1.1. Standards of length, mass and time

In 1960, an international committee established a set of standards for

the fundamental quantities of science call SI (Système International)

Length

The distance between two points in space

Standard in SI: meter (m)

1960: 1m = the length of the meter was defined as the distance

between two lines on a specific platinum–iridium bar stored under

controlled conditions in France

1960s-1970s: 1m = 1 650 763.73 wavelengths 1 of orange-red

light emitted from a krypton-86 lamp

1983: 1m = the distance traveled by light in vacuum during a time

of 1/299792458 second

PART 1: MECHANICS

12

CHAPTER 1: PHYSICS AND MEASUREMENT

1.1. Standards of length, mass and time

Mass

Standard in SI: kilogram (kg)

1987: 1kg = the mass of a specific platinum–

iridium alloy cylinder kept at the International

Bureau of Weights and Measures at Sèvres,

France

Time

Standard in SI: second (s)

1967: 1s = 9 192 631 770 times the period of

vibration of radiation from the cesium-133 atom

(in an atomic clock)

PART 1: MECHANICS

13

CHAPTER 1: PHYSICS AND MEASUREMENT

1.2. Dimentional analysis

• The dimensions of length l, mass m, and time t are L,

M, and T, respectively.

• Use brackets [ ] to denote the dimensions of a

physical quantity.

• Assume that a quantity f = g(z, y, z) is a function of

quantities x, y and z with the corresponding

dimensions [x], [y] and [z], the dimension of f:

• [f ] = g([x ], [y ], [z ])

• Example:

• The dimensions of speedv = l/t are written [v ] = L/T.

• The dimensions of area A = l × l are [A ] = L × L = L2.

PART 1: MECHANICS

14

CHAPTER 1: PHYSICS AND MEASUREMENT

1.2. Dimensional analysis

• Quantities can be added or subtracted only if they

have the same dimensions.

• The terms on both sides of an equation must have the

same dimensions.

Example 1.1. Analysis of an equation

Show that the expression , where

represents speed,

acceleration, and an instant of time, is dimensionally correct.

• Solve:

• The dimensions of v: [v] = L/T

• The dimensions of at: [at] =

• Therefore, v = at is dimensionally correct because we

have the same dimensions on both sides.

PART 1: MECHANICS

15

CHAPTER 1: PHYSICS AND MEASUREMENT

1.3. Conversion of units

Sometimes it is necessary to convert units from one measurement

system to another or convert within a system.

1 km = 1000 m, 1 m = 10 dm = 100 cm =1000 mm

1 mile (mi)= 1609 m

1 feet (ft) = 0.3048 m, 1 m = 39.37 in.

1 inch (in.) = 0.0254 m, 1 m = 3.281 ft

Example 1.3

36 km/h = ? m/s

200 mi/h = ? m/s

PART 1: MECHANICS

16

CHAPTER 1: PHYSICS AND MEASUREMENT

1.4. Estimates and Order-of-Magnitude

Calculations

•Order

of magnitude is a power often determined as follows

Example 1.4

PART 1: MECHANICS

17

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•Significant

figures is the number of numerical digits used to express

the measurement

+ 1; 2 have one significant figure; 12; 2,3 have two SF; 123; 1,56 have

three SF.

+ 1,01; 202 have three SF; 2016; 50,25 have four SF; 30001; 1,1001 have

five SF

+ 0,1; 0,002 have one SF; 0,16; 0,0025 have two SF; 0,102; 0,123 have

three SF

+ 12,00; 2,010 have four SF; 20; 2,0 have two SF; 0,100; 10,0 have three SF

+ Mass of 1500 g is an ambiguous value should use scientific notation

such as g (2 SF), or g (3 SF), or g (4 SF)

+ The same rule holds for numbers less than 1. Ex: (2 SF), (4 SF)

PART 1: MECHANICS

18

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•The

rule of determinating the number of significant figures

When multiplying several quantities, the number of significant

figures in the final answer is the same as the number of significant

figures in the quantity having the smallest number of significant

figures. The same rule applies to division

Ex: Report the result of multiplications

The area of a carpet whose length is 15.24 m and whose width is

2.19 m

The area of the disc whose radius is 6.0 cm

PART 1: MECHANICS

19

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•The

rule of determinating the number of significant figures

When numbers are added or subtracted, the number of decimal

places in the result should equal the smallest number of decimal

places of any term in the sum or difference

Ex:

Note: The rule for rounding number

The last digit retained is increased by 1 if the last digit dropped is

greater than 5 (Ex: 2.567 2.57)

If the last digit dropped is less than 5, the last digit retained remains as

it is (Ex: 2.564 2.56)

If the last digit dropped is equal to 5, the remaining digit should be

rounded to the nearest even number (Ex: 2.565 2.56, 2.555 2.56)

PART 1: MECHANICS

21

CHAPTER 2: MOTION IN ONE DIMENSION

Introduction

Kinematics: describe the motion of an object while ignoring the

interactions with external agents

Motion in one dimension: motion of an object along a straight line

Particle model: describe the moving object as a particle regardless

of its size (a particle to be a point-like object)

Physical terms

http://www.conservapedia.com/Physical_Science_Terms

motion, particle, kinematics, position, reference point, coordinate

system, velocity, speed, average/instantaneous velocity/speed,

derivative, acceleration, gravity, resistance, period, angular speed,

centripetal acceleration, tangential and radial acceleration, relative

velocity/acceleration

PART 1: MECHANICS

22

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity, speed

•Position

A particle’s position is the location of the particle with respect to

a chosen reference point that we can consider to be the origin of a

coordinate system

Example

One dimension coordinate system

Pictorial representation

Position-time graph

Graphical representation

PART 1: MECHANICS

23

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity, speed

•Displacement

and distance

The displacement of a particle is its change in position in some

time interval

As the particle moves from an initial position

displacement is given by

to a final position , its

Note: Displacement differs from distance

Displacement ()

Distance (d)

change in position

the length of a path

vector quantity

scalar quantity

Ex: After each period of motion of a particle moving in a circle of radius :

PART 1: MECHANICS

24

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity and speed

•Velocity

and speed

The average velocity of a particle is defined as the particle’s

displacement divided by the time interval during which that

displacement occurs:

Dimension: L/T

Note 1: In one dimension motion, the average velocity can be positive or

negative, depending on the sign of the displacement

Note 2: Velocity differs from speed

The average speed of a particle is defined as

PART 1: MECHANICS

25

CHAPTER 2: MOTION IN ONE DIMENSION

2.2. Instantaneous velocity and speed

•Instantaneous

velocity

The instantaneous velocity (or velocity for short) of a particle at a

particular instant in time equals the limiting value of the ratio as

approaches zero:

Note 1: The instantaneous velocity can be positive, negative, or zero

Note 2: Velocity differs from speed

The instantaneous speed (or speed for short) of a particle is defined as the

magnitude of its velocity .

PHYSICS 1: MECHANICS AND THERMODYNAMICS

PHYSICS 2: OSCILLATIONS, ELECTRICITY AND MAGNETISM

PHYSICS 3: WAVES, OPTICS AND MODERN PHYSICS

2

Introduction

1. Title: Physics 1

2. Credits: 3

3. Prerequisites:

Analytics analysis

4. Course Description

This course tends to give students opportunity to explore the basic

concepts, laws and application of Mechanics and Thermodynamics,

including:

Properties and laws of motion of particle, rigid body

Relationship among position, velocity and acceleration

Laws of linear momentum, angular momentum and energy

The kinetic theory of gases, thermodynamic quantities

Laws of Thermodynamics

3

Introduction

5. Textbook

1.

Raymond A. Serway and W. Jewett, Physics for Scientists and

Engineers with Modern Physics (9th Edition), Cengage

Learning, USA, 2014

2.

Trần Ngọc Hơi, Phạm Văn Thiều, Vật lý đại cương: Các

nguyên lý và ứng dụng, Tập 1: Cơ học và Nhiệt học, NXB Giáo

dục 2006

Reference Books

3.

Hugh D. Young and Roger A. Freedman, University Physics with

Modern Physics (13th Edition), Pearson Education, USA, 2012

4.

Paul A. Tipler and Gene Mosca, Physics for Scientists and

Engineers (6th Ed.), W. H. Freeman and Company, USA, 2008

5.

David Halliday, Cơ sở vật lý, tập 1, NXB Giáo dục, 2007

4

Introduction

6. Lesson plan

Week

1

2

3

4

Lesson

Preparation of student

Introduction

Chapter 1: Physics and measurement

Read the text book: 2-13

Chapter 2: Motion in one dimension

Read the text book: 21-47

Chapter 3: Montion in two dimensions

Read the text book: 78-98

Chapter 4: The laws of motion

Read the text book: 111-135

Solve problems of chapters 2, 3, 4

Prepare the solution of

problems by group

Chapter 5: Circular motion and other

applications of Newton’s laws

Read the text book: 150-167

Chapter 6: Energy of the system

Read the text book: 177-201

Chapter 7: Conservation of energy

Read the text book: 211-233

5

Introduction

6. Lesson plan

Week

5

6

7

8

Lesson

Preparation of student

Solve problems of chapters 5, 6, 7

Prepare the solution of

problems by group

Chapter 8: Linear momentum and

collisions

Read the text book: 247-279

Chapter 9: Rotation of rigid object about

a fiexd axis

Read the text book: 293-321

Solve problems of chapters 8, 9

Prepare the solution of

problems by group

Chapter 10: Angular momentum

Read the text book: 335-352

Chapter 11: Static equilibrium and

elasticity, Universal gravitation, Fluid

mechanics

Study by your self: 363-449

Introduction to the project of course

6

Introduction

6. Lesson plan

Week

Lesson

Preparation of student

Solve problems of chapters 10

Prepare the solution of

problems by group

Chapter 12: Tempurature and the first

law of Thermodynamics

Read the text book: 568-625

Chapter 13: The kinetic theory of gases

Read the text book: 626-652

10

Chapter 14: Heat engines, entropy and

the second law of Thermodynamics

Read the text book: 653-688

11

Solve problems of chapters 12, 13, 14

Prepare the solution of

problems by group

Represent the result of the project

Work in group to make the

product of the project and to

prepare a report of project

9

12

7

Introduction

7. Assessment Plan

Assessment Types

Assessment Components

Percentages

20%

A1. Learning activities

A1.1. Attendance

A1.2. Homework report

A1.3. Project

A2. Midterm Exam

A2.1. Written Test

20%

A3. Final Exam

A3.1. Written Test

60%

8. Student Responsibilities and Policies:

Attendance: It is compulsory that students attend at least 80%

of the course to be eligible for the final examination.

Missed tests: Students are not allowed to miss any of the tests.

There are very few exceptions

PART 1: MECHANICS

CHAPTER 1: PHYSICS AND MEASUREMENT

PHYSICS AND

MEASUREMENT

CHAPTER 1

PART 1: MECHANICS

9

CHAPTER 1: PHYSICS AND MEASUREMENT

Physics

Physics, the most fundamental physical science, is concerned with

the fundamental principles of the Universe.

The study of physics can be divided into six main areas:

Classical mechanics: concerning the motion of objects that are large

relative to atoms and move at speeds much slower than the speed of light

Relativity: a theory describing objects moving at any speed, even speeds

approaching the speed of light

Thermodynamics: dealing with heat, work, temperature, and the statistical

behavior of systems with large numbers of particles

Electromagnetism: concerning electricity, magnetism, and electromagnetic

fields

Optics: the study of the behavior of light and its interaction with materials

Quantum mechanics: a collection of theories connecting the behavior of

matter at the submicroscopic level to macroscopic observations

PART 1: MECHANICS

10

CHAPTER 1: PHYSICS AND MEASUREMENT

Physics and measurement

Like all other sciences, physics is based on experimental

observations and quantitative measurements.

Objectives: to identify fundamental laws governing natural

phenomena and use them to develop theories

Tool: Language of mathematics (a bridge between theory and

experiment)

Classical physics: includes the principles of classical mechanics,

thermodynamics, optics, and electromagnetism developed before

1900 (Newton mechanics)

Modern physics: a major revolution in physics began near the end

of the 19th century (theories of relativity and quantum mechanics)

PART 1: MECHANICS

11

CHAPTER 1: PHYSICS AND MEASUREMENT

1.1. Standards of length, mass and time

In 1960, an international committee established a set of standards for

the fundamental quantities of science call SI (Système International)

Length

The distance between two points in space

Standard in SI: meter (m)

1960: 1m = the length of the meter was defined as the distance

between two lines on a specific platinum–iridium bar stored under

controlled conditions in France

1960s-1970s: 1m = 1 650 763.73 wavelengths 1 of orange-red

light emitted from a krypton-86 lamp

1983: 1m = the distance traveled by light in vacuum during a time

of 1/299792458 second

PART 1: MECHANICS

12

CHAPTER 1: PHYSICS AND MEASUREMENT

1.1. Standards of length, mass and time

Mass

Standard in SI: kilogram (kg)

1987: 1kg = the mass of a specific platinum–

iridium alloy cylinder kept at the International

Bureau of Weights and Measures at Sèvres,

France

Time

Standard in SI: second (s)

1967: 1s = 9 192 631 770 times the period of

vibration of radiation from the cesium-133 atom

(in an atomic clock)

PART 1: MECHANICS

13

CHAPTER 1: PHYSICS AND MEASUREMENT

1.2. Dimentional analysis

• The dimensions of length l, mass m, and time t are L,

M, and T, respectively.

• Use brackets [ ] to denote the dimensions of a

physical quantity.

• Assume that a quantity f = g(z, y, z) is a function of

quantities x, y and z with the corresponding

dimensions [x], [y] and [z], the dimension of f:

• [f ] = g([x ], [y ], [z ])

• Example:

• The dimensions of speedv = l/t are written [v ] = L/T.

• The dimensions of area A = l × l are [A ] = L × L = L2.

PART 1: MECHANICS

14

CHAPTER 1: PHYSICS AND MEASUREMENT

1.2. Dimensional analysis

• Quantities can be added or subtracted only if they

have the same dimensions.

• The terms on both sides of an equation must have the

same dimensions.

Example 1.1. Analysis of an equation

Show that the expression , where

represents speed,

acceleration, and an instant of time, is dimensionally correct.

• Solve:

• The dimensions of v: [v] = L/T

• The dimensions of at: [at] =

• Therefore, v = at is dimensionally correct because we

have the same dimensions on both sides.

PART 1: MECHANICS

15

CHAPTER 1: PHYSICS AND MEASUREMENT

1.3. Conversion of units

Sometimes it is necessary to convert units from one measurement

system to another or convert within a system.

1 km = 1000 m, 1 m = 10 dm = 100 cm =1000 mm

1 mile (mi)= 1609 m

1 feet (ft) = 0.3048 m, 1 m = 39.37 in.

1 inch (in.) = 0.0254 m, 1 m = 3.281 ft

Example 1.3

36 km/h = ? m/s

200 mi/h = ? m/s

PART 1: MECHANICS

16

CHAPTER 1: PHYSICS AND MEASUREMENT

1.4. Estimates and Order-of-Magnitude

Calculations

•Order

of magnitude is a power often determined as follows

Example 1.4

PART 1: MECHANICS

17

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•Significant

figures is the number of numerical digits used to express

the measurement

+ 1; 2 have one significant figure; 12; 2,3 have two SF; 123; 1,56 have

three SF.

+ 1,01; 202 have three SF; 2016; 50,25 have four SF; 30001; 1,1001 have

five SF

+ 0,1; 0,002 have one SF; 0,16; 0,0025 have two SF; 0,102; 0,123 have

three SF

+ 12,00; 2,010 have four SF; 20; 2,0 have two SF; 0,100; 10,0 have three SF

+ Mass of 1500 g is an ambiguous value should use scientific notation

such as g (2 SF), or g (3 SF), or g (4 SF)

+ The same rule holds for numbers less than 1. Ex: (2 SF), (4 SF)

PART 1: MECHANICS

18

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•The

rule of determinating the number of significant figures

When multiplying several quantities, the number of significant

figures in the final answer is the same as the number of significant

figures in the quantity having the smallest number of significant

figures. The same rule applies to division

Ex: Report the result of multiplications

The area of a carpet whose length is 15.24 m and whose width is

2.19 m

The area of the disc whose radius is 6.0 cm

PART 1: MECHANICS

19

CHAPTER 1: PHYSICS AND MEASUREMENT

1.5. Significant figures

•The

rule of determinating the number of significant figures

When numbers are added or subtracted, the number of decimal

places in the result should equal the smallest number of decimal

places of any term in the sum or difference

Ex:

Note: The rule for rounding number

The last digit retained is increased by 1 if the last digit dropped is

greater than 5 (Ex: 2.567 2.57)

If the last digit dropped is less than 5, the last digit retained remains as

it is (Ex: 2.564 2.56)

If the last digit dropped is equal to 5, the remaining digit should be

rounded to the nearest even number (Ex: 2.565 2.56, 2.555 2.56)

PART 1: MECHANICS

21

CHAPTER 2: MOTION IN ONE DIMENSION

Introduction

Kinematics: describe the motion of an object while ignoring the

interactions with external agents

Motion in one dimension: motion of an object along a straight line

Particle model: describe the moving object as a particle regardless

of its size (a particle to be a point-like object)

Physical terms

http://www.conservapedia.com/Physical_Science_Terms

motion, particle, kinematics, position, reference point, coordinate

system, velocity, speed, average/instantaneous velocity/speed,

derivative, acceleration, gravity, resistance, period, angular speed,

centripetal acceleration, tangential and radial acceleration, relative

velocity/acceleration

PART 1: MECHANICS

22

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity, speed

•Position

A particle’s position is the location of the particle with respect to

a chosen reference point that we can consider to be the origin of a

coordinate system

Example

One dimension coordinate system

Pictorial representation

Position-time graph

Graphical representation

PART 1: MECHANICS

23

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity, speed

•Displacement

and distance

The displacement of a particle is its change in position in some

time interval

As the particle moves from an initial position

displacement is given by

to a final position , its

Note: Displacement differs from distance

Displacement ()

Distance (d)

change in position

the length of a path

vector quantity

scalar quantity

Ex: After each period of motion of a particle moving in a circle of radius :

PART 1: MECHANICS

24

CHAPTER 2: MOTION IN ONE DIMENSION

2.1. Position, velocity and speed

•Velocity

and speed

The average velocity of a particle is defined as the particle’s

displacement divided by the time interval during which that

displacement occurs:

Dimension: L/T

Note 1: In one dimension motion, the average velocity can be positive or

negative, depending on the sign of the displacement

Note 2: Velocity differs from speed

The average speed of a particle is defined as

PART 1: MECHANICS

25

CHAPTER 2: MOTION IN ONE DIMENSION

2.2. Instantaneous velocity and speed

•Instantaneous

velocity

The instantaneous velocity (or velocity for short) of a particle at a

particular instant in time equals the limiting value of the ratio as

approaches zero:

Note 1: The instantaneous velocity can be positive, negative, or zero

Note 2: Velocity differs from speed

The instantaneous speed (or speed for short) of a particle is defined as the

magnitude of its velocity .

## Bài giảng quản lý chất lượng công trường

## Bài giảng Quản lý chất lượng

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 10 ppsx

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 9 pps

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## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 7 pot

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 6 pps

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 5 pptx

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 4 potx

## Thiết kế bài giảng vật lý 11 nâng cao tập 2 part 3 ppsx

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