hinojosa (jlh3938) – oldmidterm1 01 – Turner – (58185)
1
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printout
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have
20
questions.
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before answering.
001
10.0 points
Consider a piece of string which is placed
along the
x
axis.
Let Δ
m
be the mass of a
segment of the string and Δ
x
the length of
this segment. The linear mass density,
μ
, of a
piece of string is defined as
μ
=
Δ
m
Δ
x
.
Denote
ρ
to be its mass density defined as
ρ
=
mass
volume
and
A
its cross sectional area. Let us write
μ
=
ρ
x
A
y
.
Using dimensional analysis,
determine the
equations which enable one to solve for
x
and
y
.
1.
x
= 1
,
2
y
−
3
x
= 1
2.
x
= 1
,
3
x
+ 2
y
= 1
3.
x
=
−
1
,
2
y
+ 3
x
=
−
1
4.
x
= 1
,
2
y
+ 3
x
=
−
1
5.
x
=
−
1
,
2
y
−
3
x
= 1
6.
x
=
−
1
,
2
y
−
3
x
=
−
1
7.
x
= 1
,
−
2
y
−
3
x
=
−
1
8.
x
= 1
,
2
y
−
3
x
=
−
1
correct
9.
x
=
−
1
,
3
x
+ 2
y
= 1
10.
x
=
−
1
,
−
2
y
−
3
x
=
−
1
Explanation:
[
μ
] = [
ρ
x
A
y
]
ML
−
1
=
M
x
L
−
3
x
L
2
y
=
M
x
L
2
y
−
3
x
Equating both sides yields the equations
x
= 1
,
2
y
−
3
x
=
−
1
002
10.0 points
Two points in a rectangular coordinate sys
tem have the coordinates (4
.
6 cm, 5
.
9 cm) and
(
−
8
.
8 cm, 4
.
5 cm).
Find the distance between these points.
Correct answer: 13
.
4729 cm.
Explanation:
Given :
x
1
= 4
.
6 cm
,
y
1
= 5
.
9 cm
,
x
2
=
−
8
.
8 cm
,
and
y
2
= 4
.
5 cm
.
Using the Pythagorean Theorem,
d
=
radicalBig
(Δ
x
)
2
+ (Δ
y
)
2
=
radicalBig
(
x
2
−
x
1
)
2
+ (
y
2
−
y
1
)
2
=
radicalBig
[4
.
6 cm
−
(
−
8
.
8 cm)]
2
+ (4
.
5 cm
−
5
.
9 cm)
2
=
13
.
4729 cm
.
003
10.0 points
Ann is driving down a street at 64 km
/
h.
Suddenly a child runs into the street.
If it takes Ann 0
.
718 s to react and apply
the brakes, how far will she have moved before
she begins to slow down?
Correct answer: 12
.
7645 m.
Explanation:
d
=
v t
= (64 km
/
h) (0
.
718 s)
= 12
.
7645 m
.
Dimensional analysis
for
d
:
km
h
·
s
1
·
1 h
3600 s
·
1000 m
3600 km
= m
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hinojosa (jlh3938) – oldmidterm1 01 – Turner – (58185)
2
004
10.0 points
The graph shows position as a function of
time for two trains running on parallel tracks.
At time
t
= 0 (origin) the position of both
trains is 0.
position
time
t
B
B
A
Which is true?
1.
Both trains speed up all the time
2.
Both trains have the same velocity at
some time before
t
B
correct
3.
Somewhere before time
t
B
, both trains
have the same acceleration
4.
At time
t
B
, both trains have the same
velocity
5.
In the time interval from
t
=0 to
t
=
t
B
,
train B covers more distance than train A
Explanation:
The slope of the curve B is parallel to line
A at some point
t < t
B
.
005
10.0 points
Suppose the position equation for a moving
object is given by
s
(
t
) = 3
t
2
+ 2
t
+ 5
where
s
is measured in meters and
t
is mea
sured in seconds.
Find the velocity of the object when
t
= 2.
1.
13 m/sec
2.
14 m/sec
correct
3.
10 m/sec
4.
6 m/sec
5.
None of these
Explanation:
s
(
t
) = 3
t
2
+ 2
t
+ 5
The velocity is
v
(
t
) =
s
′
(
t
) = 6
t
+ 2
and
v
(2) = 14.
006
10.0 points
A ranger in a national park is driving at
49 km
/
h when a deer jumps onto the road
61 m ahead of the vehicle.
After a reaction
time of
t
s, the ranger applies the brakes to
produce an acceleration of
−
3
.
8 m/s
2
.
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 Fall '08
 Turner
 Acceleration, Velocity, Correct Answer, Hinojosa

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