PHYS 1443 – Section 001 Lecture #1

PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

1Monday, June 6, 2011

PHYS 1443 – Section 001Lecture #1

Monday, June 6, 2011Dr. Jaehoon Yu

• Class Introduction• Standard and units• Dimensional Analysis• Fundamentals• One Dimensional Motion: Average Velocity;

Acceleration; Motion under constant acceleration; Free Fall

Today’s homework is homework #1, due 10pm, Wednesday, June 8!!

Monday, June 6, 2011 PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

2

Announcements• Reading assignment #1: Read and follow through

all sections in appendices A and B by Wednesday, June 8– There will be a quiz this Wednesday, June 8, on this

reading assignment


3

Special Problems for Extra Credit• Derive the quadratic equation for Bx2-Cx+A=0

5 points• Derive the kinematic equation

from first principles and the known kinematic equations 10 points

• You must show your work in detail to obtain full credit

• Due at the start of the class, Thursday, June 9

ifxf xxavv xxi 222


4

Who am I?• Name: Dr. Jaehoon Yu (You can call me Dr. Yu)• Office: Rm 342, Chemistry and Physics Building

– Office Hours: 2:30 – 3:30pm Mondays and Wednesdays or by appointment• Extension: x22814, E-mail: [email protected] • My profession: High Energy Particle Physics (HEP)

– Collide particles (protons on anti-protons or electrons on anti-electrons, positrons) at the energies equivalent to 10,000 Trillion degrees

– To understand• Fundamental constituents of matter• Interactions or forces between the constituents• Origin of Mass• Creation of Universe (Big Bang Theory)

– A pure scientific research activity• Direct use of the fundamental laws we find may take longer than we want but • Indirect product of research contribute to every day lives; eg. WWW

mailto:[email protected]

Monday, June 6, 2011

We always wonder…• What is the universe made of?• How does the universe work?• What are the things that holds the universe

together?• What are the governing principles of the

universe?• How can we live in the universe well?• Where do we all come from?• HEP looks into the smallest possible things to

find the answers to these deep questionsPHYS 1443-001, Spring 2011 Dr.

Jaehoon Yu5


The Standard Model of Particle Physics • Prescribes the following fundamental structure:

• Three families of leptons and quarks together with 12 force mediators Simple and elegant!!!

• Tested to a precision of 1 part per million!

~0.01mp

Family

Discovered in 1995, ~170mp

Directly observed in 2000


6


Good, but still lots we don’t know…• Why are there three families of quarks and leptons?• Why is the mass range so large (0.01mp – 175 mp)?• How do matters acquire mass?

– Higgs mechanism but where is the Higgs, the God particle?• Why is the matter in the universe made only of particles?

– What happened to anti-particles? Or anti-matters?• Why are there only three apparent forces?• Is the picture we present the real thing?

– What makes up the 96% of the universe?– How about extra-dimensions?

• How is the universe created? • Are there any other theories that describe the universe better?

– Does the super-symmetry exist?


7


8

Accelerators are Powerful Microscopes.

They make high energy particle beams that allow us to see small things.

seen byhigh energy beam(better resolution)

seen bylow energy beam

(poorer resolution)


9

Accelerators are also Time Machines.

E = mc2

They make particles last seen in the earliest moments of the universe.

Energy

Particle and anti-particle annihilate.

particle beam

energy

anti-particle beam

energy


Fermilab Tevatron and LHC at CERN• World’s Highest Energy proton-anti-proton collider

– 6km circumference– Ecm=1.96 TeV (=6.3x10-7J/p 13M Joules on 10-

4m2)– Equivalent to the kinetic energy of a 20t truck at the

speed 81mi/hr 130km/hr• ~100,000 times the energy density at ground 0 of the atom

bomb dropped on Hiroshima– To be shut down Sept. 30, 2011

Chicago

Tevatron p

p CDF DØ

• World’s Highest Energy p-p collider– 27km circumference, 100m underground– Design Ecm=14 TeV (=44x10-7J/p 362M

Joules on the area less than 10-4m2) Equivalent to the kinetic energy of a B727

(80tons) at the speed 193mi/hr 312km/hr ~3M times the energy density at ground 0 of atom

bomb dropped on Hiroshima• First 7TeV collisions on 3/30/10 The highest energy

humans ever achieved!!• First collisions in 2011 in mid March, 2011


10


11

LHC @ CERN Aerial View

Geneva Airport

ATLAS

CMS

France

Swizerland


A Future Linear Collider• An electron-positron collider on a straight line for precision

measurements• CMS Energy: 0.5 – 1 TeV• 10~15 years from now• Takes 10 years to build the accelerator and the detector

L~31km


12

Circumference ~6.6km~310 soccer fields


13

DØ Detector

30’

30’

50’

ATLAS Detector

• Weighs 5000 tons and 5 story tall• Can inspect 3,000,000 collisions/second• Record 100 collisions/second• Records approximately 10,000,000 bytes/second• Records 0.5x1015 (500,000,000,000,000) bytes

per year (0.5 PetaBytes).

• Weighs 7000 tons and 10 story tall• Can inspect 1,000,000,000 collisions/second• Records 200 – 400 collisions/second• Records approximately 350,000,000

bytes/second• Will record 2x1015 (2,000,000,000,000,000)

bytes each year (2 PetaByte).


14

DØ Central Calorimeter 1990


15

Computers put together a picture

Digital data

Data Reconstruction

`pp


16qTim

ep p

q g

K

“par

ton

jet”

“par

ticle

jet”

“cal

orim

eter

jet”

hadrons

CH

FH

EM

Highest ET dijet event at DØ

0.69 GeV, 472E

0.69 GeV, 475E21

T

11T

How does an Event Look in a Collider Detector?

http://www-d0online.fnal.gov/www/shift/event_pix.html




17

GEM Application Potential FAST X-RAY IMAGING

Using the lower GEM signal, the readout can be self-triggered with energy discrimination:

A. Bressan et al, Nucl. Instr. and Meth. A 425(1999)254F. Sauli, Nucl. Instr. and Meth.A 461(2001)47

9 keV absorption radiography of a small mammal (image size ~ 60 x 30 mm2)

And in not too distant future, we could do …

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Information & Communication Source• My web page: http://www-hep.uta.edu/~yu/

– Contact information & Class Schedule– Syllabus– Homework– Holidays and Exam days– Evaluation Policy– Class Style & Communication– Other information

• Office Hours: 10:00 – 11:00am, Mondays through Thursdays or by appointments

http://www-hep.uta.edu/~yu/


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Evaluation Policy• Homework: 30%• Exams

– Midterm and Final Comprehensive Exams (6/21 and 7/11): 22.5% each– Missing an exam is not permissible unless pre-approved

• No makeup test!!• You will get an F if you miss any of the exams without a

prior approval• Lab score: 15%• Pop-quizzes: 10%• Extra credits: 10% of the total

– Random attendances– Strong participation in the class discussions– Special projects– Planetarium shows and Other many opportunities

• Grading will be done on a sliding scale

100%


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Homework• Solving homework problems is the only way to comprehend class

material• An electronic homework system has been setup for you

– Details are in the material distributed today and on the web– https://quest.cns.utexas.edu/student/courses/list – Choose the course PHYS1443-001-SUMMER2011, unique number 43111– Download homework #1, solve the one problem and submit them online– Multiple unsuccessful tries will deduct points– Roster will close at midnight Wednesday, June 8– You need a UT e-ID: Go and apply at the URL

https://idmanager.its.utexas.edu/eid_self_help/?createEID&qwicap-page-id=EA027EFF7E2DA39E if you don’t have one.

• Each homework carries the same weight• ALL homework grades will be used for the final grade• Home work will constitute 30% of the total A good way of keeping

your grades high• Strongly encouraged to collaborate Does not mean you can copy

https://quest.cns.utexas.edu/student/courses/list

https://idmanager.its.utexas.edu/eid_self_help/?createEID&qwicap-page-id=EA027EFF7E2DA39E

https://idmanager.its.utexas.edu/eid_self_help/?createEID&qwicap-page-id=EA027EFF7E2DA39E


22

Attendances and Class Style• Attendances:

– Will be taken randomly– Will be used for extra credits

• Class style:– Lectures will be on electronic media

• The lecture notes will be posted on the web AFTER each class– Will be mixed with traditional methods– Active participation through questions and discussions are

STRONGLY encouraged Extra credit….– Communication between you and me is extremely

important• If you have problems, please do not hesitate talking to me


23

Lab and Physics Clinic• Physics Labs:

– Starts, Wed. June 8, 2011– Important to understand physical principles through experiments– 15% of the grade– Lab syllabus is available in your assigned lab rooms.

• Go by the lab room between 8am - 6pm M – F and pick up the syllabus • Physics Clinic:

– Room SH007, 12 – 6pm Mon – Thur and 1 – 6pm Sat. – Free of charge– They provide general help on physics, including help solving homework problems

• Do not expect solutions of the problem from them!• Do not expect them to tell you whether your answers are correct!• It is your responsibility to make sure that you have done everything correctly!

– Will let you know via e-mail when the service begins

Extra credit• 10% addition to the total

–Could boost a B to A, C to B or D to C• What constitute for extra credit?

–Random attendances–Physics department colloquium participation

• Some will be double or triple credit (–Strong participation in the class discussions–Special projects–Watch the valid planetarium shows–Many other opportunities


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Valid Planetarium Shows• Regular running shows

– Magnificent Sun– Violent Universe– Wonders of the Universe

• Shows that need special arrangements– Stars of the Pharaohs– Black Holes– Two small pieces of glass– SOPHIA

• How to submit for extra credit?– Obtain the ticket stub that is signed and dated by the planetarium star

lecturer of the day– Collect the ticket stubs– Tape all of them on a sheet of paper with your name and ID written on it– Submit the sheet at the end of the semester when asked


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What can you expect from this class?• All A’s?

– This would be really nice, wouldn’t it?– But if it is too easy it is not fulfilling or meaningful….

• This class is not going to be a stroll in the park!! (Very fast pace!!)• You will earn your grade in this class.

– You will need to put in sufficient time and sincere efforts– Exams and quizzes will be tough!!

• Sometimes problems might not look exactly like what you learned in the class• Just putting the right answer in free response problems does not work!

• But you have a great control of your grade in your hands– Homework is 30% of the total grade!!

• Means you will have many homework problems– Sometimes much more than any other classes– Sometimes homework problems will be something that you have yet to learn in class

– Lab 15%– Extra credit 10%

• I will work with you so that your efforts are properly awarded


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What do we want to learn in this class?• Physics is everywhere around you.• Understand the fundamental principles that surrounds you in

everyday lives…• Identify what laws of physics applies to what phenomena and

use them appropriately• Understand the impact of such physical laws• Learn how to research and analyze what you observe.• Learn how to express observations and measurements in

mathematical language• Learn how to express your research in systematic manner in

writing• I don’t want you to be scared of PHYSICS!!!

Most importantly, let us have a lot of FUN!!

Monday, June 6, 2011 28PHYS 1443-001, Spring 2011 Dr. Jaehoon Yu

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Why do Physics?• To understand nature through experimental

observations and measurements (Research)• Establish limited number of fundamental laws, usually

with mathematical expressions• Predict the nature’s course⇒ Theory and Experiment work hand-in-hand⇒ Theory works generally under restricted conditions⇒ Discrepancies between experimental measurements

and theory are good for improvements⇒ Improves our everyday lives, even though some laws

can take a while till we see them amongst us

Exp.{Theory {


29

Brief History of Physics• AD 18th century:

– Newton’s Classical Mechanics: A theory of mechanics based on observations and measurements

• AD 19th Century:– Electricity, Magnetism, and Thermodynamics

• Late AD 19th and early 20th century (Modern Physics Era)– Einstein’s theory of relativity: Generalized theory of space, time, and energy

(mechanics)– Quantum Mechanics: Theory of atomic phenomena

• Physics has come very far, very fast, and is still progressing, yet we’ve got a long way to go – What is matter made of?– How do matters get mass?– How and why do matters interact with each other?– How is universe created?


30

Models, Theories and Laws• Models: An analogy or a mental image of a phenomena in

terms of something we are familiar with– Thinking light as waves, behaving just like water waves– Often provide insights for new experiments and ideas

• Theories: More systematically improved version of models– Can provide quantitative predictions that are testable and

more precise• Laws: Certain concise but general statements about how

nature behaves – Energy conservation– The statement must be found experimentally valid to become a law

• Principles: Less general statements of how nature behaves– Has some level of arbitrariness

Monday, June 6, 2011 3131

Uncertainties• Physical measurements have limited precision,

however good they are, due to:– Number of measurements – Quality of instruments (meter stick vs micro-meter)– Experience of the person doing measurements– Etc

• In many cases, uncertainties are more important and difficult to estimate than the central (or mean) values

Stat.{

{Syst.



Significant Figures• Denote the precision of the measured values

– The number 80 implies precision of +/- 1, between 79 and 81• If you are sure to +/-0.1, the number should be written 80.0

– Significant figures: non-zero numbers or zeros that are not place-holders• 34, 34.2, 0.001, 34.100

– 34 has two significant digits– 34.2 has 3– 0.001 has one because the 0’s before 1 are place holders to position “.”– 34.100 has 5, because the 0’s after 1 indicates that the numbers in these digits

are indeed 0’s.• When there are many 0’s, use scientific notation for simplicity:

– 31400000=3.14x107

– 0.00012=1.2x10-4



Significant Figures• Operational rules:

– Addition or subtraction: Keep the smallest number of decimal place in the result, independent of the number of significant digits: 12.001+ 3.1=

– Multiplication or Division: Keep the smallest number of significant difits in the result: 12.001 x 3.1 = , because the smallest significant figures is ?.

15.1

37

What does this mean? The worst precision determines the precision the overall operation!!


Can’t get any better than the worst measurement!

In English?


34

Needs for Standards and Units• Seven basic quantities for physical measurements

– Length, Mass, Time, Electric Current, Temperature, the Amount of substance and Luminous intensity

• Need a language that everyone can understand each other– Consistency is crucial for physical measurements– The same quantity measured by one must be comprehendible

and reproducible by others– Practical matters contribute

• A system of unit called SI (System Internationale) was established in 1960– Length in meters (m)– Mass in kilo-grams (kg)– Time in seconds (s)


35

Definition of Three Relevant Base Units

One second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 (C133) atom.

1 s (Time)

It is equal to the mass of the international prototype of the kilogram, made of platinum-iridium in International Bureau of Weights and Measure in France.

1 kg (Mass) =

1000 g

One meter is the length of the path traveled by light in vacuum during the time interval of 1/299,792,458 of a second.

1 m (Length) = 100 cm

DefinitionsSI Units

• There are total of seven base quantities (see table 1-5 on page 7)• There are prefixes that scales the units larger or smaller for convenience (see pg. 7)• Units for other quantities, such as Newtons for force and Joule for energy, for ease of use


36

Prefixes, expressions and their meanings

• deci (d): 10-1

• centi (c): 10-2

• milli (m): 10-3

• micro (μ): 10-6

• nano (n): 10-9

• pico (p): 10-12

• femto (f): 10-15

• atto (a): 10-18

• zepto (z): 10-21

• yocto (y): 10-24

• deca (da): 101

• hecto (h): 102

• kilo (k): 103

• mega (M): 106

• giga (G): 109

• tera (T): 1012

• peta (P): 1015

• exa (E): 1018

• zetta (Z): 1021

• yotta (Y): 1024

Larger Smaller


37

International Standard Institutes

• International Bureau of Weights and Measure http://www.bipm.fr/– Base unit definitions:

http://www.bipm.fr/enus/3_SI/base_units.html – Unit Conversions: http://www.bipm.fr/enus/3_SI/

• US National Institute of Standards and Technology (NIST) http://www.nist.gov/

http://www.bipm.fr/

http://www.bipm.fr/enus/3_SI/base_units.html

http://www.bipm.fr/enus/3_SI/

http://www.nist.gov/


38

How do we convert quantities from one unit to another?

Unit 1 = Unit 2Conversion factor X1 inch 2.54 cm1 inch 0.0254 m1 inch 2.54x10-5 km

1 ft 30.3 cm1 ft 0.303 m1 ft 3.03x10-4 km1 hr 60 minutes1 hr 3600 seconds

And many More Here….


2

2

0.0929 m1 ft


39

Examples 1.3 and 1.4 for Unit Conversions• Ex 1.3: An apartment has a

floor area of 880 square feet (ft2). Express this in square meters (m2).

2880 ft

2880 0.0929 m

2880 ft

Ex 1.4: Where the posted speed limit is 55 miles per hour (mi/h or mph), what is this speed (a) in meters per second (m/s) and (b) kilometers per hour (km/h)?

1 mi=

55 mi/h (a)

2880 ft

What do we need to know?

212in1ft

5280 ft 1609 m 1.609 km 12 in1 ft

2.54 cm1 in

1 m100cm

55 mi 25 m/s 1609 m

1 mi

1 1 h

1 h3600 s

20.0254 m1 i

n

282m

55 mi/h (b) 55 mi =88 km/hr 1.609km

1 mi

1 1 h


40

Estimates & Order-of-Magnitude Calculations • Estimate = Approximation

– Useful for rough calculations to determine the necessity of higher precision

– Usually done under certain assumptions– Might require modification of assumptions, if higher

precision is necessary• Order of magnitude estimate: Estimates done to the

precision of 10s or exponents of 10s;– Three orders of magnitude: 103=1,000– Round up for Order of magnitude estimate; 8x107 ~ 108

– Similar terms: “Ball-park-figures”, “guesstimates”, etc


41

Example 1.8

2 2 2R h d R

2 2

2d hR

h

2 2 2 22R hR h d R

Estimate the radius of the Earth using triangulation as shown in the picture when d=4.4km and h=1.5m.

R

d=4.4km

R+h

Pythagorian theorem

Solving for R

2 24400 1.52 1.5

6500

m mm

km


Dimension and Dimensional Analysis• An extremely useful concept in solving physical problems• Good to write physical laws in mathematical expressions• No matter what units are used the base quantities are the

same– Length (distance) is length whether meter or inch is used to

express the size: Usually denoted as [L]– The same is true for Mass ([M])and Time ([T])– One can say “Dimension of Length, Mass or Time”– Dimensions are treated as algebraic quantities: Can perform two

algebraic operations; multiplication or division



Dimension and Dimensional Analysis• One can use dimensions only to check the

validity of one’s expression: Dimensional analysis– Eg: Speed [v] = [L]/[T]=[L][T-1]

• Distance (L) traveled by a car running at the speed V in time T

– L = V*T = [L/T]*[T]=[L]• More general expression of dimensional analysis

is using exponents: eg. [v]=[LnTm] =[L][T-1] where n = 1 and m = -1



Examples• Show that the expression [v] = [at] is dimensionally correct

• Speed: [v] =[L]/[T]• Acceleration: [a] =[L]/[T]2

• Thus, [at] = (L/T2)xT=LT(-2+1) =LT-1 =[L]/[T]= [v]

2 m mnvkra

Dimensionlessconstant

Length Speed

1 2LT

rvvkra

221

r va

n m

• Suppose the acceleration a of a circularly moving particle with speed v and radius r is proportional to rn and vm. What are n andm?

m

n LLT

n m mL T

m 22n 1 n 1



Some Fundamentals• Kinematics: Description of Motion without understanding the cause

of the motion• Dynamics: Description of motion accompanied with understanding

the cause of the motion• Vector and Scalar quantities:

– Scalar: Physical quantities that require magnitude but no direction • Speed, length, mass, height, volume, area, magnitude of a vector quantity, etc

– Vector: Physical quantities that require both magnitude and direction• Velocity, Acceleration, Force, Momentum• It does not make sense to say “I ran with velocity of 10miles/hour.”

• Objects can be treated as point-like if their sizes are smaller than the scale in the problem– Earth can be treated as a point like object (or a particle)in celestial problems

• Simplification of the problem (The first step in setting up to solve a problem…)– Any other examples?



Some More Fundamentals• Motions:Can be described as long as the position is

known at any given time (or position is expressed as a function of time)– Translation: Linear motion along a line– Rotation: Circular or elliptical motion– Vibration: Oscillation

• Dimensions– 0 dimension: A point– 1 dimension: Linear drag of a point, resulting in a line

Motion in one-dimension is a motion on a line– 2 dimension: Linear drag of a line resulting in a surface– 3 dimension: Perpendicular Linear drag of a surface, resulting

in a stereo object



47

Displacement, Velocity and SpeedOne dimensional displacement is defined as:

ixxx f

The average velocity is defined as: xv

The average speed is defined as: Total Distance Traveled

Total Elapsed Timev

f

f

i

i

x xt t

xt

Displacement per unit time in the period throughout the motion

Displacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance?

DisplacementElapsed Time

Unit? m/s

Unit? m

Unit? m/s

A vector quantity

A scalar quantity

A vector quantity


48

How much is the elapsed time? t= t 0- t

1x 2x

What is the displacement? =x 2x 1- x


49

Displacement, Velocity and SpeedOne dimensional displacement is defined as:

ixxx f

The average velocity is defined as: xv

The average speed is defined as: Total Distance Traveled

Total Elapsed Timev

Can someone tell me what the difference between speed and velocity is?

f

f

i

i

x xt t

xt

Displacement per unit time in the period throughout the motion

Displacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance?

DisplacementElapsed Time

Unit? m/s

Unit? m

Unit? m/s


Difference between Speed and Velocity• Let’s take a simple one dimensional translation

that has many steps:Let’s call this line as X-axis

Let’s have a couple of motions in a total time interval of 20 sec.

+10m +15m

-15m-5m -10m

+5m

Total Displacement: x

Total Distance Traveled: D

Average Velocity: f

f

ix

i

x xvt t

Average Speed: Total Distance TraveledTotal Time Interval

v

xt

020

0( / )m s

≡xf −xi i ix x 0( )m

10 15 5 15 10 5 60( )m

6020

3( / )m s



Example 2.1

2 1f ix x x x x • Displacement:

• Average Velocity: f

f

ix

i

x xvt t

• Average Speed: Total Distance Traveled

Total Time Intervalv

The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x1=50.0m to x2=30.5 m, as shown in the figure. What was the runner’s average velocity? What was the average speed?

30.5 50.0 19.5( )m

2 1

2 1

x x xt t t

19.5 6.50( / )

3.00m s

50.0 30.5 19.5 6.50( / )3.00 3.00

m s



52

Instantaneous Velocity and Speed• Can average quantities tell you the detailed story of

the whole motion?

xxvt

Δt 0lim

*Magnitude of Vectors are Expressed in absolute values

• Instantaneous speed is the size (magnitude) of the velocity vector:

xxvt

Δt 0lim

• Instantaneous velocity is defined as:– What does this mean?

• Displacement in an infinitesimal time interval• Average velocity over a very, very short amount of time

NO!!


535353

Instantaneous Velocity

Time

Average Velocity

Instantaneous Velocity


545454

Position vs Time Plot

timet1 t2 t3t=0

Position

x=0

x11 2 3

1. Running at a constant velocity (go from x=0 to x=x1 in t1, Displacement is + x1 in t1 time interval)

2. Velocity is 0 (go from x1 to x1 no matter how much time changes)3. Running at a constant velocity but in the reverse direction as 1. (go

from x1 to x=0 in t3-t2 time interval, Displacement is - x1 in t3-t2 time interval)

It is helpful to understand motions to draw them on position vs time plots.

Does this motion physically make sense?


55


565656

Example 2.3

2x 1x

xv

x

(a) Determine the displacement of the engine during the interval from t1=3.00s to t2=5.00s.

Displacement is, therefore:

A jet engine moves along a track. Its position as a function of time is given by the equation x=At2+B where A=2.10m/s2 and B=2.80m.

(b) Determine the average velocity during this time interval.

1 3.00tx 22.10 (3.00) 2.80 21.7m 2 5.00tx 22.10 (5.00) 2.80 55.3m

2 1x x 55.3 21.7 33.6 m

xt

33.6

5.00 3.00

33.6 16.8 /

2.00m s


575757

Example 2.3 cont’d

1 nn nCtCtdtd

5.00xv t s

xv At2

Calculus formula for derivative

The derivative of the engine’s equation of motion is

(c) Determine the instantaneous velocity at t=t2=5.00s.

and 0Cdtd

The instantaneous velocity at t=5.00s is

0lim

t

xt

dxdt

2d At Bdt

2 5.00A 2.10 10.0 21.0 /m s


585858

Displacement, Velocity and Speed

dtdx

txvx

lim0Δt

Displacement ixxx f

Average velocity tx

ttxxvi

ix

f

f

Average speed Spent Time TotalTraveled Distance Total

v

Instantaneous velocity

Instantaneous speed dtdx

txvx

lim0Δt


59

Acceleration

• In calculus terms: The slope (derivative) of the velocity vector with respect to time or the change of slopes of position as a function of time

xa xv analogous to

xa dtdx

txvx

lim0Δt

analogous to

Change of velocity in time (what kind of quantity is this?)• Definition of the average acceleration:

• Definition of the instantaneous acceleration:

xf

f

xi

i

v vt t

xvt

f

f

i

i

x xt t

xt

xvt

Δt 0lim xdv

dt d dx

dt dt

2

2

d xdt

Vector


60

Acceleration vs Time Plot

What does this plot tell you?Yes, you are right!!The acceleration of this motion is a constant!!


61

Example 2.4

xa )/(2.40.5

210.5

021 2sm

A car accelerates along a straight road from rest to 75km/h in 5.0s.

What is the magnitude of its average acceleration?

xfv

xiv

)/(105.41000

36002.4 242

hkm

0 /m s

750003600

ms

21 /m s

xf xi

f i

v vt t

xvt


62

Few Confusing Things on Acceleration• When an object is moving in a constant velocity (v=v0), there is

no acceleration (a=0)– Is there any acceleration when an object is not moving?

• When an object is moving faster as time goes on, (v=v(t) ), acceleration is positive (a>0).– Incorrect, since the object might be moving in negative direction initially

• When an object is moving slower as time goes on, (v=v(t) ), acceleration is negative (a<0)– Incorrect, since the object might be moving in negative direction initially

• In all cases, velocity is positive, unless the direction of the movement changes.– Incorrect, since the object might be moving in negative direction initially

• Is there acceleration if an object moves in a constant speed but changes direction?

The answer is YES!!

Date post:	09-Feb-2016
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PHYS 1443 – Section 001 Lecture #1

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