Distance vs. Displacement,
Velocity,
Speed vs Velocity,
and
Velocity vs Acceleration
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Everything in the Everything in the universe is in motion.
universe is in motion.
How do we know?
How do we know?
David is in Motion
Motion
Megan is in Motion
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Everything in the Everything in the universe is in motion.
universe is in motion.
How do we know?
How do we know?
World is rotating
World is rotating
Motion
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Everything in the universe is in motion.
How do we know?
World is rotating
World is revolving
Motion
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Everything in the universe is in motion.
How do we know?
World is rotating
World is revolving
The Solar System is revolving around a galactic center
Motion
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Everything in the universe is in motion.
How do we know?
World is rotating
World is revolving
The Solar System is revolving around a galactic center
The Universe is expanding
Motion
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Everything in the universe is in motion.
How do we know?
World is rotating
World is revolving
The Solar System is revolving around a galactic center
The Universe is expanding
Motion is Relative
Motion
Hi Dad! Hi Mom!
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E
NC
RE
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Motion
FE
RE
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Everything in the universe is in motion.
How do we know?
World is rotating
World is revolving
The Solar System is revolving around a galactic center
The Universe is expanding
Motion is Relative
Everything has its own reference frame ﴾Shout out to Einstein﴿
NOTES...LIVE AND IN COLOR!!!
I would suggest you take notes like this:
Motion:
Speed:
• Measure of how fast something is moving
• Speed = Distance
Time
• Speed is a rate: “something divided by time”
Motion:
Distance:
How far you travel.
Displacement:
How far you are from where you began (your POSITION).
SPEED Example:
S = 12 m/s t = 10. s
d = ???
Given:
Find: • SI units for Speed: (m/s)
Instantaneous Speed vs Average Speed
t x Savg = Instantaneous Speed – speed at any given moment of time
d
x t t
d = St
d = (12 m/s)(10. s) = 120 m
St = d
Average Speed – total distance covered over a time interval
Acceleration:
Speed is scalar (magnitude but no direction)
Velocity is a vector (magnitude and direction)
2﴿ Savg = d t
Savg = average speed
1﴿ Vector Magnitude & Direction
2﴿ vavg = d t
vavg = average velocity
t = time
t = time
m Change in velocity
Change in time
s2
Gravity is an acceleration
Gravity = 9.8 m/s2 ACCELERATION Example:
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is
its acceleration? m
v2 ­ v1
/s Δv
30 m/s ­ 25 m/s
a = =
= = 2.5 s
­ t
t
1
2
2.0 s ­ 0.0 s
Δt
m
d = distance
/s d = DISPLACEMENT
Ways to Accelerate:
­Speed up
­Slow down
­Change direction
Units:
Δt
Velocity:
Speed:
1﴿ Scalar Magnitude only
a = Δv
UNITS:
UNITS:
s
==
m
s
xx
1
s
==
m
s2
a = 2.5 m/s2
• Measure of how fast something is moving
• Measure of how fast something is moving
• Speed = Distance
Time
• Measure of how fast something is moving
• Speed = Distance
Time
• Speed is a rate: “something divided by time”
Measure of how fast something is moving
• Measure of how fast something is moving
• Speed = Distance
Time
Speed is a rate: “something divided by time”
• Speed is a rate: “something divided by time”
• SI units for Speed: (m/s)
Instantaneous Speed – speed at any given moment of time
Instantaneous Speed – speed at any given moment of time
Average Speed – total distance covered over a time interval
Instantaneous Speed – speed at any given moment of time
Average Speed – total distance covered over a time interval
Instantaneous Speed – speed at any given moment of time
Average Speed – total distance covered over a time interval
Speed is scalar (magnitude but no direction)
Instantaneous Speed – speed at any given moment of time
Average Speed – total distance covered over a time interval
Speed is scalar (magnitude but no direction)
Velocity is a vector (magnitude and direction)
Who says direction
doesn't matter?
1m / s
OR
1m / s
Speed:
Velocity:
1) Scalar Magnitude 1﴿ Vector Magnitude only
& Direction
2) Savg = d t
2﴿ vavg = d t
Savg = average speed
vavg = average velocity
t = time
t = time
d = distance
d = DISPLACEMENT
What's the Difference???
Distance:
How far you travel.
Displacement:
How far you are from where you began ﴾your POSITION﴿.
What distance
did I travel?
Distance or
Displacement
?
SPEED
Title Page
1
Need for Speed:
1. If Usain Bolt can maintain a constant 1)
speed of 12 m/s, he will cover 12 meters every second. At this rate, how far will he travel in 10. seconds?
Need for Speed:
1. If Usain Bolt can maintain a constant 1)
speed of 12 m/s, he will cover 12 meters every second. At this rate, how far will he travel in 10. seconds?
d
t x Savg = x t t
St = d
d = St
d = (12 m/s)(10. s) = 120 m
2 Need for Speed:
2. If Usain Bolt can maintain a constant 2)
speed of 12 m/s, he will cover 12 meters every second. At this rate, how far will he travel in 1 minute?
Need for Speed:
2. If Usain Bolt can maintain a constant 2)
speed of 12 m/s, he will cover 12 meters every second. At this rate, how far will he travel in 1 minute?
1 min x
60 s
1 min
( ) = 60 s
d = St
d = (12 m/s)(60 s) = 720 m
Title Page
a = ∆v / ∆t Change in velocity
Change in time
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
­Speed up
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
­Speed up
­Slow down
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
­Speed up
­Slow down
­Change direction
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
­Speed up
­Slow down
­Change direction
Units:
a = ∆v / ∆t Change in velocity
Change in time
Ways to Accelerate:
­Speed up
­Slow down
­Change direction
Units:
m s22
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? Use 2 SIG­FIGS!!!
1 If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? v
Δ
a = Δtt
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? v v2 ­ v1
Δ
=
a = t 2 ­ t 1
Δtt
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? m
m
v
­ v
30 /s ­ 25 /s v
s
1
2
Δ
=
=
a = t 2 ­ t 1
2.0 s ­ 0.0 s
.0 s ­ 0.0 s
Δtt
2
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? m
m
m
v
­ v
/s 30 /s ­ 25 /s v
2
1
s
Δ
=
=
= 2.5 s a = t2 ­ t1
2.0 s ­ 0.0 s
.0 s ­ 0.0 s
Δtt
2
s
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? m
m
m
v
­ v
/s 30 /s ­ 25 /s v
2
1
s
Δ
=
=
= 2.5 s a = t2 ­ t1
2.0 s ­ 0.0 s
.0 s ­ 0.0 s
Δtt
2
s
m
/s UNITS: ss If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? m
m
m
v
­ v
/s 30 /s ­ 25 /s v
2
1
s
Δ
=
=
= 2.5 s a = t2 ­ t1
2.0 s ­ 0.0 s
.0 s ­ 0.0 s
Δtt
2
s
m
1
m
/s s x
UNITS:
=
s
s
s
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration? m
m
m
v
­ v
/s 30 /s ­ 25 /s v
2
1
s
Δ
=
=
= 2.5 s a = t2 ­ t1
2.0 s ­ 0.0 s
.0 s ­ 0.0 s
Δtt
2
s
m
1
m
m
/s s x
= 2
UNITS:
=
s
s
s
s
m
m
If my car accelerates from 25 /s to 30 /s in 2.0 seconds, what is its acceleration? m
m
m
v
­ v
/s 30 /s ­ 25 /s v
2
1
s
Δ
= 2.5 s =
=
a = 2.0 s ­ 0.0 s
t2 ­ t1
.0 s ­ 0.0 s
Δtt
s
2
m
m
m x 1
/s s UNITS:
=
=
2
s
s
s
s
m
m
a = 2.5 /ss22
Gravity is an:
v
Δ
a = Δt
2
Gravity = 9.8 m/s
Gravity is constant on Earth. It causes the same rate of acceleration for ALL falling objects.
DEMO TIME:
If I drop these at the same time, the constant acceleration of gravity implies they should hit the ground at the same time. Will they???
DEMO TIME:
HOW ABOUT NOW???