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•
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•
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•
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take the survey
on Moodle
•
Labs
and
discussions
have
already
started
Objectives
•
Relate distance, velocity, and acceleration.
•
Interpret distance

time, velocity

time, and
acceleration

time plots.
Describing Motion
It’s all math today
The Tortoise and the Hare
Told in words,
formulas, and
graphs
Poll Question
Who was faster?
A.
The
tortoise
.
B.
The
hare
.
C.
They had the
same
speed.
D.
What do you mean by faster?
Group Work: Graph
1.
Describe the Tortoise

and

hare race
using a
position

time graph.
•
Same axes
•
One world

line for tortoise, another for hare
•
Indicate significant times and positions
Speed
average
speed =
D
d
D
t
over
entire interval
instantaneous
speed = lim
D
d
D
t
at
one instant
D
t
0
Rate of changing position
Speed as Slope
Speed =
D
distance
D
time
distance
time
= slope of graph!
D
d
D
t
Poll Question
Who had the highest
average
speed
overall?
A.
The
tortoise
.
B.
The
hare
.
C.
Their average speeds were the
same
.
Poll Question
Who had the highest
instantaneous
speed?
A.
The
tortoise
.
B.
The
hare
.
C.
Their instantaneous
speeds were the
same
.
D.
At what time?
Example: Quantify
If we know definite distance and time values:
a.
What distance was the course?
b.
When did the hare stop?
c.
When did the hare wake?
d.
When did the tortoise finish?
We can calculate velocities.
Speed Units
distance
time
=
m/s
Group Work: Graph
2.
Describe the Tortoise

and

hare race
using a
velocity

time graph.
Distance Change as Area
•
What are the
areas
under the tortoise’s
and hare’s velocity

time plots?
speed
time
t
1
t
2
t
3
hare
tortoise
area
=
v
D
t
=
D
(
distance)
t
0
t
4
Group Work: Graph
3.
A car waits at a stop light for 5
seconds,
smoothly
accelerates
to 15
m/s over
5
seconds, and then continues at 15
m/s.
Describe the car’s motion using a
velocity

time
graph.
Acceleration
Rate of changing velocity
average
acceleration =
D
v
D
t
over the
entire interval
instantaneous
acceleration = lim
D
v
D
t
D
t
0
at
one instant
Acceleration Units
velocity
time
=
s
m/s
=
m/s
2
Group Work: Graph
4.
What is the car’s
acceleration
at the
different times? Describe the car’s
motion using an
acceleration

time graph.
Group Work: Compute
5.
How
far
does the car go:
a.
Between 0
s and 5
s?
b.
Between 10
s and 15
s?
Acceleration
Starting from a traffic light that turns green
d
t
v
t
a
t
area
=
velocity
area
=
distance
slope
=
velocity
slope
=
acceleration
Group Work 6
Describe four ways:
time
position
0
Group Work 6
Describe four ways:
time
velocity
0
Group Work 6
Describe four ways:
time
acceleration
0
Group Work 6
Describe four ways:
A coconut hangs motionless from its tree,
then drops with increasing downward speed
until it lands on the ground, quickly coming
to rest.
Formulas for Constant
Acceleration
•
Velocity change
D
v
=
a
D
t
•
Velocity
v
t
=
v
0
+
D
v
=
v
0
+
a
D
t
•
Position change
D
x
=
v
0
D
t
+ 1/2
a
(
D
t
)
2
•
Position
x
t
=
x
0
+
v
0
D
t
+ 1/2
a
(
D
t
)
2
Reading for Next Time
•
Vectors
: how we handle quantities with
directions
•
Important vectors:
position
,
velocity
,
acceleration
,
force
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