Physical quantities. Units. Kinematics....
Transcript of Physical quantities. Units. Kinematics....
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Lecture 1Lecture 1
Physical quantities. Units. Kinematics. Velcity.
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Welcome to Physics 111Welcome to Physics 111
About myself● Mohamad Al-Saqer● Office: 209 Phyics Hall● Phone: 294-9361● Office Hours:
● MWRT 1:15 PM-2:15 PM.● Or by appointment.
● Research:Theoretical Physics in NanomagneticMolecules and computation.
![Page 3: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/3.jpg)
The Physics 111 Instructor TeamThe Physics 111 Instructor Team● Lecturer:
● Dr. Mohamad Al-Saqer 12:10-1:10
● Course secretary:● Deb Schmidt. Room 12 Physics.
● Lab supervisor:● Dr. Paula Herrera-Siklody. Room 15 Physics.
● Recitation and Lab TAs: Separate sheet are provided in the course website.
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The syllabus● Linked from Physics course web page:
http://course.physastro.iastate.edu/phys111● and in Canvas course page.● Contains all the information needed for the course:
● Contact info.● Lecture and course timeline.● Homework, recitation and grading policy info.● Lab info (more about lab in a separate Canvas page.)● etc.
Zeroth! Homework Assignment:Read the Syllabus carefully.
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Exams:
● 3 mid-semester exams at lecture time:
➔Final exam
Monday, June 25 12:10pm – 1:10pmMonday, July 9 12:10pm – 1:10pmMonday, July 23 12:10pm – 1:10pm
Friday, Aug 3 11:00am – 1:00pm
Make no other plans for these times
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Recitations & Homework
● Tue Wed Thur Fri (60 minutes)
● Quizzes: Last 15 minutes of Wed and Fri recitations. Except first week (only Friday) and last week (Only Wednesday)
● Online homework will be linked from Canvas.● There is an introductory to MasteringPhysics assignment
(optional for no credit) to get you familiarized with the interface.
● First homework is due Tuesday 6/12 midnight.
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Labs● 14 two-hour labs● Each section meets every week.● Prelab must be completed before corresponding lab.● Check lab schedule for dates and time of your session.● Detailed lab info on Canvas separate page.● For questions regarding labs, e-mail Paula Herrera (
[email protected]).Questions based on material covered in recitations and labs will be on the final exam!
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How to succeed in Physics 111Physics can only be learned by doing it(just like swimming, bike riding or becoming a mechanic)
● Lectures● Prepare for lecture.
● Read the indicated assignments before class ● Attend actively.
● Ask questions, participate in interactive problems● Homework
● Do all problems● Review the HW solutions● Understand and learn from your mistakes.● Reflect on the problems you've done right.
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How does Physics work?How does Physics work?
Observe and
measure
Build a model
Make a prediction
math
math
math
math
math math
check
units
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SI UnitsSI Units
Length: The meter (1 m = 3.281 ft)
Mass: The kilogram (1 kg = 0.06585 slug)Not the same as weight!
on Earth 1 kg weighs 2.205 lbon the Moon 1 kg weighs 0.368 lb
Time: The second (s)
Standard International Units are used by scientific and engineering communities and almost everywhere in the world.
The British System is used in the USA
Combinations:Unit of speed m/s Unit of force (Newton) is 1 N =1 kg m/s²
Other systems: mks (meter-kilogram-second)cgs (centimeter-gram-secos)
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Multiples of UnitsMultiples of Units10-24 yocto- y10-21 zepto- z10-18 atto- a10-15 femto- f10-12 pico- p10-9 nano- n10-6 micro-
10-3 milli- m10-2 centi- c103 kilo- k106 mega- M109 giga- G1012 tera- T1015 peta- P1018 exa- E1021 zetta- Z1024 yotta- Y
Formal conversion of units:
•Multiply by the appropriate representation of 1 to cancel the unwanted units away:
•eg. convert 10 mph into m/s
10 mile 1 h
= 10 mile 1 h
×1 h
3600 s×
1609 m mile
= 4.47 m/s
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Consistency of EquationsConsistency of Equations
If A=B then A and B must have the same combination of units (dimensionality).
• For example (distance)=(speed)(time) [m] = ([m]/[s]) [s]
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ACT: Dimensional AnalysisACT: Dimensional Analysis The period T of a swinging pendulum depends only
on the length of the pendulum d and the acceleration of gravity, g. Which of the following formulas could be correct?
A.
C. 2 dT gp=
d
Note: [Acceleration] = m/s2
T = 2π (dg )2 T = 2π(dg )
2
B.
D.T = 2π√ gd
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ACT: Dimensional AnalysisACT: Dimensional Analysis The period T of a swinging pendulum depends only
on the length of the pendulum d and the acceleration of gravity, g. Which of the following formulas could be correct?
A.
C. 2 dT gp=
d
Note: [Acceleration] = m/s2
T = 2π (dg )2 T = 2π(dg )
2
B.
D.T = 2π√ gd
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ACT: Converting AreaACT: Converting AreaAn area of 3.0 ft2 in System international is:
note (1 m = 3.281 ft)
A. 280 m2
C. 0.028 m2
B. 2800 m2
D. 0.28 m2
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ACT: Converting AreaACT: Converting AreaAn area of 3.0 ft2 in System international is:
note (1 m = 3.281 ft)
A. 280 m2
C. 0.028 m2
B. 2800 m2
D. 0.28 m2
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Significant figures
When we measure something, there’s a limited accuracy: result error (or accuracy, or uncertainty)
Example 1: 2.35 0.01
Example 2: Imagine I write: 2.35 0.1 . Does this make sense? No!Wrong: 2.35 0.1Correct: 2.4 0.1
Example 1: 0.24630
1sf 0.22sf 0.253sf 0.2464sf 0.24635sf 0.24630
Example 2: Not so clear in some cases: 200 (1,2,3 ?)
Scientific notation is crystal clear: 2 102 (or 0.2 103) 1sf2.0 102 (or 0.20 103) 2sf2.00 102 (or 0.200 103) 3sf
Measurement and uncertaintyMeasurement and uncertainty
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Significant figures ...continuedSignificant figures ...continued
A distance measured with a ruler with millimeter markings cannot be 1.047543 m
The last three digits are meaningless
Keep track of that in calculationsEg. Find the distance covered by a car moving at 31.6 mph for 35 minutes.
Correct value is 1.047 m (4 significant figures)
=1 h35 min 0.583 h
60 minLast digit is meaningless, but you can keep it until last step…
Correct answer is 18 miles (only 2 significant figures given for time)
distance = 31.6miles
h≈0.583h = 18.4miles
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Scientific notation and significant figuresScientific notation and significant figures
Number Significant figures
3.4 2
3.40 / 3.45 3
0.3 / 3 / 0.0003 1
30 1 or 2?
3101 1
3.0101 2
3.00101 3
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Order of magnitudeOrder of magnitude
• Intuition: A coin is dropped from 2 m. How long does it take to reach the ground?
→ About 1 s. (not 10 s, not 0.1 s)
• Estimation:
Example: The roof in room 5 is a 10 m x 20 m flat surface. If the drains get clogged and 1 cm of water accumulates on it, this is an extra
How “strong” should a roof be?
Not 200 kg, not 20,000 kg
200 m2 × 0.01 m × (1000 kg1 m3 ) = 2000 kg (4410 lb)
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An overview of Mechanics An overview of Mechanics
Mechanics: study of the motion of objects. 1. Kinematics: How do objects move?
2. Dynamics: Why do objects move?
4. Some special cases:•Rigid body motion
•Simple harmonic motion
•Gravitational forces, Hooke’s law…
3. Conservation laws:•Work-energy
•Momentum (linear and angular)
For some problems, the math is easier to handle with
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The Simplest Case: The Simplest Case: 1D Motion along a Straight Line1D Motion along a Straight Line
Position: A single + or – number (coordinate) describes the location of an object relative to a reference point (origin).
Description of motion: position x as a function of time t:
An equation x(t)A graphA table of data
Time (t)
Position (x)
tA
xA
tB
xB
tE
xE
tD
xD ,
tC
xC
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Displacement: Change in position ΔxAB = xB − xA
Displacement over a fixed time period only tells us about the “result” of the motion (not the path).
ΔxAB > 0ΔxBD < 0ΔxAD = 0 !!!
Time (t)
Position (x)
tA
xA
tB
xB
tD
xD ,
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VelocityVelocity
= rate of change of position
txv
=
Simplest idea: For displacement of Δx over a time Δt :
Average velocity
Unit: m/s
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xvt
=
!!!
Not a very good description of what really happened!Problem: Our time intervals are too large and too many things are happening in between.
t
x
AB
D
For Δ t = tB−tA → v > 0For Δ t = tD−tB → v < 0For Δ t = tD−tA → v = 0
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E
t
x
A
C
D
B
It is the slope of
the x(t) curve.
Instantaneous VelocityInstantaneous Velocity
vC = 0
Solution: take limit Δt 0.→
vA > 0
vB > 0 ( |vB|>|vA| )
vD < 0
vE < 0
v = limΔ t → 0
Δ x
Δ T
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Motion with Constant velocity: Motion with Constant velocity: GraphicsGraphics
v =Δ x
Δ t
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Example: Graph of motion: Speed vs. TimeExample: Graph of motion: Speed vs. Time
v =Δ x
Δ t
va =24 m−12 m
10 s−4 s= 2 m/s
vb =24 m−24 m
20 s−10 s=
0
10 s=0
vc =4 m−24 m
30 s−20 s=
−20 m
10 s=−2 m/s
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3- What speed we are reading on the speedometer: average or instantaneous?
Velocity versus speedVelocity versus speed
Velocity = vector (value including sign, in 1D)
Speed = magnitude of velocity (always positive)
The speedometer of the truck #1 moving to the east reads 90 km/h. It passes another truck, #2, that moves to the west at 90 km/h.1- Do both trucks have the same velocity? NO2- Do both trucks have the same speed? Yes
Instantaneous
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Velocity versus speedVelocity versus speed
A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.
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Velocity versus speedVelocity versus speed
A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.
|vAmes to Des Moines|=50 km
0.5 h=100 km/h
|vDes Moines to Ames|=50 km
0.5 h=100 km/h
vAmes to Des Moines back to Ames=50 km+(−50 km)
0.5 h+0.5 h=
0
1 h=0 km/hRound trip
velocity:
|vAmes to Des Moines back to Ames|=50 km+50 km
0.5 h+0.5 h=100 km/hRound trip
speed:
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Lecture 1Lecture 1
Physical quantities. Units. Kinematics. Velcity.
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Welcome to Physics 111Welcome to Physics 111
About myself● Mohamad Al-Saqer● Office: 209 Phyics Hall● Phone: 294-9361● Office Hours:
● MWRT 1:15 PM-2:15 PM.● Or by appointment.
● Research:Theoretical Physics in NanomagneticMolecules and computation.
![Page 34: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/34.jpg)
The Physics 111 Instructor TeamThe Physics 111 Instructor Team● Lecturer:
● Dr. Mohamad Al-Saqer 12:10-1:10
● Course secretary:● Deb Schmidt. Room 12 Physics.
● Lab supervisor:● Dr. Paula Herrera-Siklody. Room 15 Physics.
● Recitation and Lab TAs: Separate sheet are provided in the course website.
![Page 35: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/35.jpg)
How to succeed in Physics 111Physics can only be learned by doing it(just like swimming, bike riding or becoming a mechanic)
● Lectures● Prepare for lecture.
● Read the indicated assignments before class ● Attend actively.
● Ask questions, participate in interactive problems● Homework
● Do all problems● Review the HW solutions● Understand and learn from your mistakes.● Reflect on the problems you've done right.
![Page 36: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/36.jpg)
How does Physics work?How does Physics work?
Observe and
measure
Build a model
Make a prediction
math
math
math
math
math math
check
units
![Page 37: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/37.jpg)
SI UnitsSI Units
Length: The meter (1 m = 3.281 ft)
Mass: The kilogram (1 kg = 0.06585 slug)Not the same as weight!
on Earth 1 kg weighs 2.205 lbon the Moon 1 kg weighs 0.368 lb
Time: The second (s)
Standard International Units are used by scientific and engineering communities and almost everywhere in the world.
The British System is used in the USA
Combinations:Unit of speed m/s Unit of force (Newton) is 1 N =1 kg m/s²
Other systems: mks (meter-kilogram-second)cgs (centimeter-gram-secos)
![Page 38: Physical quantities. Units. Kinematics. Velcity.course.physastro.iastate.edu/...units_kinematics...SI Units Length: The meter (1 m = 3.281 ft) Mass: The kilogram (1 kg = 0.06585 slug)](https://reader034.fdocuments.us/reader034/viewer/2022042402/5f10e9dc182ac61e843326d7/html5/thumbnails/38.jpg)
Multiples of UnitsMultiples of Units10-24 yocto- y10-21 zepto- z10-18 atto- a10-15 femto- f10-12 pico- p10-9 nano- n10-6 micro-
10-3 milli- m10-2 centi- c103 kilo- k106 mega- M109 giga- G1012 tera- T1015 peta- P1018 exa- E1021 zetta- Z1024 yotta- Y
Formal conversion of units:
•Multiply by the appropriate representation of 1 to cancel the unwanted units away:
•eg. convert 10 mph into m/s
10 mile 1 h
= 10 mile 1 h
×1 h
3600 s×
1609 m mile
= 4.47 m/s
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Consistency of EquationsConsistency of Equations
If A=B then A and B must have the same combination of units (dimensionality).
• For example (distance)=(speed)(time) [m] = ([m]/[s]) [s]
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ACT: Dimensional AnalysisACT: Dimensional Analysis The period T of a swinging pendulum depends only
on the length of the pendulum d and the acceleration of gravity, g. Which of the following formulas could be correct?
A.
C. 2 dT gp=
d
Note: [Acceleration] = m/s2
T = 2π (dg )2 T = 2π(dg )
2
B.
D.T = 2π√ gd
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ACT: Converting AreaACT: Converting AreaAn area of 3.0 ft2 in System international is:
note (1 m = 3.281 ft)
A. 280 m2
C. 0.028 m2
B. 2800 m2
D. 0.28 m2
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Significant figures
When we measure something, there’s a limited accuracy: result error (or accuracy, or uncertainty)
Example 1: 2.35 0.01
Example 2: Imagine I write: 2.35 0.1 . Does this make sense? No!Wrong: 2.35 0.1Correct: 2.4 0.1
Example 1: 0.24630
1sf 0.22sf 0.253sf 0.2464sf 0.24635sf 0.24630
Example 2: Not so clear in some cases: 200 (1,2,3 ?)
Scientific notation is crystal clear: 2 102 (or 0.2 103) 1sf2.0 102 (or 0.20 103) 2sf2.00 102 (or 0.200 103) 3sf
Measurement and uncertaintyMeasurement and uncertainty
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Significant figures ...continuedSignificant figures ...continued
A distance measured with a ruler with millimeter markings cannot be 1.047543 m
The last three digits are meaningless
Keep track of that in calculationsEg. Find the distance covered by a car moving at 31.6 mph for 35 minutes.
Correct value is 1.047 m (4 significant figures)
1 h35 min 0.583 h
60 minLast digit is meaningless, but you can keep it until last step…
Correct answer is 18 miles (only 2 significant figures given for time)
distance = 31.6miles
h×0.583h = 18.4miles
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Scientific notation and significant figuresScientific notation and significant figures
Number Significant figures
3.4 2
3.40 / 3.45 3
0.3 / 3 / 0.0003 1
30 1 or 2?
3101 1
3.0101 2
3.00101 3
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Order of magnitudeOrder of magnitude
• Intuition: A coin is dropped from 2 m. How long does it take to reach the ground?
→ About 1 s. (not 10 s, not 0.1 s)
• Estimation:
Example: The roof in room 5 is a 10 m x 20 m flat surface. If the drains get clogged and 1 cm of water accumulates on it, this is an extra
How “strong” should a roof be?
Not 200 kg, not 20,000 kg
200 m2 × 0.01 m × (1000 kg1 m3 ) = 2000 kg (4410 lb)
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An overview of Mechanics An overview of Mechanics
Mechanics: study of the motion of objects. 1. Kinematics: How do objects move?
2. Dynamics: Why do objects move?
4. Some special cases:•Rigid body motion
•Simple harmonic motion
•Gravitational forces, Hooke’s law…
3. Conservation laws:•Work-energy
•Momentum (linear and angular)
For some problems, the math is easier to handle with
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The Simplest Case: The Simplest Case: 1D Motion along a Straight Line1D Motion along a Straight Line
Position: A single + or – number (coordinate) describes the location of an object relative to a reference point (origin).
Description of motion: position x as a function of time t:
An equation x(t)A graphA table of data
Time (t)
Position (x)
tA
xA
tB
xB
tE
xE
tD
xD ,
tC
xC
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Displacement: Change in position ΔxAB = xB − xA
Displacement over a fixed time period only tells us about the “result” of the motion (not the path).
ΔxAB > 0ΔxBD < 0ΔxAD = 0 !!!
Time (t)
Position (x)
tA
xA
tB
xB
tD
xD ,
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VelocityVelocity
= rate of change of position
txv
=
Simplest idea: For displacement of Δx over a time Δt :
Average velocity
Unit: m/s
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xvt
=
!!!
Not a very good description of what really happened!Problem: Our time intervals are too large and too many things are happening in between.
t
x
AB
D
For Δ t = tB−tA → v > 0For Δ t = tD−tB → v < 0For Δ t = tD−tA → v = 0
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E
t
x
A
C
D
B
It is the slope of
the x(t) curve.
Instantaneous VelocityInstantaneous Velocity
vC = 0
Solution: take limit Δt 0.→
vA > 0
vB > 0 ( |vB|>|vA| )
vD < 0
vE < 0
v = limΔ t → 0
Δ x
Δ T
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Motion with Constant velocity: Motion with Constant velocity: GraphicsGraphics
v =Δ x
Δ t
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Example: Graph of motion: Speed vs. TimeExample: Graph of motion: Speed vs. Time
v =Δ x
Δ t
va =24 m−12 m
10 s−4 s= 2 m/s
vb =24 m−24 m
20 s−10 s=
0
10 s=0
vc =4 m−24 m
30 s−20 s=
−20 m
10 s=−2 m/s
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3- What speed we are reading on the speedometer: average or instantaneous?
Velocity versus speedVelocity versus speed
Velocity = vector (value including sign, in 1D)
Speed = magnitude of velocity (always positive)
The speedometer of the truck #1 moving to the east reads 90 km/h. It passes another truck, #2, that moves to the west at 90 km/h.1- Do both trucks have the same velocity? NO2- Do both trucks have the same speed? Yes
Instantaneous
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Velocity versus speedVelocity versus speed
A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.
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Velocity versus speedVelocity versus speed
A car traveled 0.5 h from Ames to Des Moines. Then it traveled 0.5 h from Des Moines to Ames. The distance traveled in each direction is 50 km. Find the average speed and velocity.
|vAmes to Des Moines|=50 km
0.5 h=100 km/h
|vDes Moines to Ames|=50 km
0.5 h=100 km/h
vAmes to Des Moines back to Ames=50 km+(−50 km)
0.5 h+0.5 h=
0
1 h=0 km/hRound trip
velocity:
|vAmes to Des Moines back to Ames|=50 km+50 km
0.5 h+0.5 h=100 km/hRound trip
speed: