Today’s Topics
• Position
• Velocity and Speed
• Acceleration
• s-v-a Graphs
O



s 2  s1  s
Speed
s
Average Speed





  
s  s 2  s1
Position
 Location on a ________relative to a _____________.
Position vector
___________________
Vector or scalar?
Positive, negative, or either?
Measured over a __________ time
Useful for ______________
Instantaneous Speed
 Vector from the __________ to the _________
 Magnitude
 Direction - can be _________ or _________
 Measured over _______________ time interval
 What you get ____________________ for
 Value shown on _________________
Displacement vector
 _______ in position of an object
 Vector or scalar?
Review: what is a position vector?
What is a displacement vector?
EF 151 Spring, 2017 Lecture 1-5
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Velocity
EF 151 Spring, 2017 Lecture 1-5
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Speed/Velocity Examples
Average Velocity
vavg 
1. You drive for ½ hr at 30 mph, and then ½ hr at 60 mph. What is
your average speed?
s s 2  s 2

t t 2  t1
 Change in ________ divided by change in _____
 Scalar or vector?
 Depends only on _________ position and _________ position
2. You drive for 30 miles at 30 mph, and then 30 miles at 60 mph. What
is your average speed?
Instantaneous Velocity
s ds
v  lim

Derivative
t 0 t
dt
3. You drive 16 miles west at an average speed of 32 mph and then
drive east at an average speed of at 40 mph in 0.3 hours.
a. What is your average speed?
Dimensions
 __________ per ____________
 Exact Conversion
b. What is your average velocity?
mi 5280 ft
hr
60mph  60

hr mi 3600 sec
EF 151 Spring, 2017 Lecture 1-5
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EF 151 Spring, 2017 Lecture 1-5
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Acceleration
Acceleration Examples
Average Acceleration
1. You start from rest and are going 30 mph after 10 seconds. What
was your average acceleration?
• Change in _________ divided by change in _________
• Scalar or vector?
Δ ̅
Δ
• Describes how the ___________ is changing
̅
̅
2. You start from rest, accelerate to 30 mph in 10 seconds, and then
brake to a stop in 2 seconds. What was your average acceleration
while braking?
Instantaneous Acceleration
v dv

t dt
Dimensions
• ________ per ________ = ________ per ________
3. What was your average acceleration during for the entire 12
seconds?
What are valid units for acceleration?
Time rate of change of acceleration is _________
Graph Example
Time
(sec)
Acceleration
(ft/sec/sec)
Time
(sec)
Slope of tangent line
(derivative)
Velocity:
 Slope: _________________

Area: _________________

Sign: __________________
Velocity
Acceleration:
 Area: ________________
 Sign:
 same as velocity:
_______________
 opposite velocity:
_______________
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EF 151 Spring, 2017 Lecture 1-5
Slope:_________________
Slope of tangent line
(derivative)
Position
(ft)
Velocity
(ft/sec)
Time
(sec)
7
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Position
Position
Acceleration
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Position
Position

EF 151 Spring, 2017 Lecture 1-5
EF 151 Spring, 2017 Lecture 1-5
(integral)
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Velocity
(integral)
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Area = change in
position
EF 151 Spring, 2017 Lecture 1-5
4. How far did you travel on this trip?
Area = change in
velocity
t 0
Curvature (2nd derivative)
a  lim
Acceleration
http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/motgraph.html
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