1
Review for
Exam 1
Review for
Exam 1
Example
Example
What tank level would indicate an average speed of 90 mph?
a.
3/4 full
b. 1/2 full
c.
1/4 full
d. 1/8 full
e.
empty
MOM, YOUR CAR
HOLDS HOW MANY
HOLDS HOW MANY
GALLONS OF GAS?
AND IT GETS HOW
MANY MILES PER
GALLON?
ABOUT
15.
ABOUT
25.
AND WAS YOUR GAS
AND WAS YOUR GAS
TANK FULL WHEN
TANK FULL WHEN
PETER TOOK IT TO
PETER TOOK IT TO
RUN ERRANDS?
RUN ERRANDS?
AND PETER HAD
IT OUT FOR HOW
LONG?
YES.
MAYBE
MAYBE
TWO
TWO
HOURS
AND THE
TANK IS
TANK IS
HALF FULL
NOW?
NOW?
LET ME GO
CHECK.
WELL,
SOMEBODY
TOLD HER HOW
FAST I WAS
FAST I WAS
DRIVING!
DON
’T LOOK
T LOOK
AT ME.
AT ME.
SO YOU
’RE
RE
GROUNDED FOR
HOW
HOW
MANY
CENTURIES?
CENTURIES?
=
=− =
1 gallon
90 miles
2 hours
7.2 gallons (used)
1 h
25 miles
gas left
15
7.2
7.8 gallons (left)
Example: Dot product
Which pair of vectors will have the largest value for
A
·
B
?
a
A
B
c
A
B

A
=
B
=5

A
=
B
=5
b
A
B

A
=
B
=5
60°
d
A
B

A
=
B
=3
30°
e
A
B

A
=
B
=3
10°
A
·
B = 0
A
·
B = 25 cos60 = 12.5
A
·
B = 0
A
·
B = 9cos30 (< 9 < 12.5)
A
·
B = 9cos10 (< 9 < 12.5)
Example: 1D motion
An object moves along the
x
axis as follows:
(
t
) = 25 + (10 m/s)
– (30m/s
3
)
t
3
a) At what time (
> 0) does the object stop?
Velocity = 0
=⇒
−
=
==
2
0
10 90
0
10
0.33 s
90
vt
()
−
32
( )
10 m/s
90 m/s
dx t
dt
a. 0 s
b. 0.33 s
c. 3.3 s
d. 10 s
e. 33 s
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Example: Free fall
A. 3.3 m
B.
9.8 m
C. 120 m
D. 240 m
E. 480 m
A ball is thrown vertically up into the air
(hard!) and
comes back down to its starting position 14 s later. At
the highest point of its trajectory, how high was the
ball?
t
0
= 0
v
0
?
y
0
= 0
top
= 0
top
?
f
= 14 s
f
?
f
= 0
A ball is thrown vertically up into the air
(hard!) and comes back down to
its starting position 14 s later. At the highest point of its trajectory,
how high above the starting position was the ball?
0
= 0
0
?
0
= 0
top
= 0
top
?
f
= 14 s
f
?
f
= 0
target
22
0
2
vv
gy
−=
−∆
To find
top
, I can use:
?
2
00
1
2
yvt gt
=+ −
[
Use
for the final situation:
2
0
2
0
1
2
(9.8 m/s )(14 s)
68.6 m/s
ff
f
vt
gt
=+
−
==
=
]
Then,
()
top
0
2
2
0
top
2
020
68.6 m/s
240 m
(
9
.
8
m
/
s
)
vg
g
−
−
=
(Answer D)
a. 2.5 s
b. 5.0 s
c. 10 s
d. 20 s
e. 40 s
Example: Projectiles
A projectile is fired from a cannon at a 30degree angle with the
ground and an initial velocity of 100 m/s. Assuming no air resistance
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 Fall '06
 Johnson
 Physics, Force, Friction, m/s, Gallon

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