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Distance vs. Displacement,
Speed vs Velocity, and
Velocity vs Acceleration
Distance vs. Displacement,
Speed vs Velocity, and
Velocity vs Acceleration
MotionMotionMotion
Megan is in MotionDavid is in
Motion
• Everything in the universe is in motion.How do we know?
• Everything in the universe is in motion.How do we know?
MotionMotionMotion• Everything in the universe is in motion.How do we know?
• World is rotating
• Everything in the universe is in motion.How do we know?
• World is rotating
MotionMotionMotion• Everything in the universe is in motion.How do we know?
• World is rotating• World is revolving
• Everything in the universe is in motion.How do we know?
• World is rotating• World is revolving
• 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
MotionMotionMotion• 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
MotionMotionMotion• 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
• 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
MotionMotionMotion• 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
Hi Dad! Hi Mom!
REFERENCEMotionMotionMotion• 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﴿
Motion: Speed:• Measure of how fast something is moving • Speed =
• Speed is a rate: “something divided by time”
• SI units for Speed: (m/s)
DistanceTime
Velocity is a vector (magnitude and 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)
Instantaneous Speed vs Average Speed
1﴿ Scalar Magnitude only
2﴿ Savg =
Savg = average speed
t = time
d = distance
d t
1﴿ Vector Magnitude & Direction
2﴿ vavg =
vavg = average velocity
t = time
d = DISPLACEMENT
d t
Speed: Velocity:
Motion:Distance:How far you travel.
Displacement:How far you are from where you began (your POSITION).
Units:
s2
m Ways to Accelerate:Speed upSlow downChange direction
Acceleration:
Change in velocityChange in time
a = ΔvΔt
Gravity is an accelerationGravity = 9.8 m/s2
SPEED Example:
ACCELERATION Example:
I would suggest you take notes like this:
Savg = dt x t t x
St = d
d = Std = (12 m/s)(10. s) = 120 m
Given: S = 12 m/s t = 10. sFind: d = ???
a = 2.5 m/s2==m/s s
mxx s
1== s2
ms
m/s
2.5 =30 m/s 25 m/s 2.0 s 0.0 s
=v2 v1 t2 t1
ΔvΔt
a = = s
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what isits acceleration?
UNITS:UNITS:
• Measure of how fast something is moving• Measure of how fast something is moving• Measure of how fast something is moving
• Measure of how fast something is moving
• Speed =
• Measure of how fast something is moving
• Speed =
• Measure of how fast something is moving
• Speed = DistanceTimeDistanceTime
DistanceTime
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
DistanceTime
DistanceTime
DistanceTime
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
• SI units for Speed: (m/s)
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
• SI units for Speed: (m/s)
• Measure of how fast something is moving
• Speed =
• Speed is a rate: “something divided by time”
• SI units for Speed: (m/s)
DistanceTime
DistanceTime
DistanceTime
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)
Velocity is a vector (magnitude and 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)
Speed: Velocity:1) Scalar Magnitude
only
2) Savg =
Savg =
t = time
d = distance
d t
1﴿ Vector Magnitude & Direction
2﴿ vavg =
vavg =
t = time
d = DISPLACEMENT
d taverage velocityaverage speed
Distance:How far you travel.
Displacement:How far you are from where you
began ﴾your POSITION﴿.
What's the Difference???
1) If Usain Bolt can maintain a constant 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.
1
1) If Usain Bolt can maintain a constant speed of 12 m/s, he will cover 12 meters every second. At this rate, how far will he travel in 10. seconds?
1.
Need for Speed:
Savg = dt x t t x
St = d
d = St
d = (12 m/s)(10. s) = 120 m
2) If Usain Bolt can maintain a constant 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.
2
2) If Usain Bolt can maintain a constant 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.
1 min x 60 s1 min = 60 s
d = St
d = (12 m/s)(60 s) = 720 m
( )
Ways to Accelerate:Ways to
Accelerate:
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Ways to Accelerate:Speed up
Ways to Accelerate:Speed up
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Ways to Accelerate:Speed upSlow down
Ways to Accelerate:Speed upSlow down
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Ways to Accelerate:Speed upSlow downChange direction
Ways to Accelerate:Speed upSlow downChange direction
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Units:Units:
Ways to Accelerate:Speed upSlow downChange direction
Ways to Accelerate:Speed upSlow downChange direction
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Units:
s2 m Units:
s2 m
Ways to Accelerate:Speed upSlow downChange direction
Ways to Accelerate:Speed upSlow downChange direction
a = ∆v / ∆t a = ∆v / ∆t
Change in velocityChange in time
Change in velocityChange in time
Use 2 SIGFIGS!!!Use 2 SIGFIGS!!!
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
1
ΔvΔtΔvΔta = a =
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
v2 v1t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
= 2.5 2.5 =30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
= 2.5 2.5 =30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
UNITS:UNITS:
==
m/s ssm/s
= 2.5 2.5 =30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
mssm xx 1
ss1UNITS:UNITS:
==
m/s ssm/s
= 2.5 2.5 =30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
mssm xx 1
ss1 == m
s2 s2
mUNITS:UNITS:
a = 2.5 m/s2a = 2.5 m/s2
==
m/s ssm/s
= 2.5 2.5 =30 m/s 25 m/s 30 m/s 25 m/s 2.0 s 0.0 s2.0 s 0.0 s==v2 v1
t2 t1v2 v1t2 t1
ΔvΔtΔvΔta = a = ==
If my car accelerates from 25 m/s to 30 m/s in 2.0 seconds, what is its acceleration?
m/s ssm/s
mssm xx 1
ss1 == m
s2 s2
mUNITS:UNITS:
Gravity is constant on Earth. It causes the same rate of acceleration for ALL falling objects.
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???