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33
Chapter 2
Motion in One Dimension
Conceptual Problems
1
•
Determine the Concept
The "average velocity" is being requested as opposed to "average
speed".
The average velocity is defined as
the change in position or
displacement divided by the
change in time.
t
y
v
∆
∆
=
av
The change in position for any
"round trip" is zero by definition.
So the
average
velocity
for any
round trip must also be zero.
0
0
av
=
∆
=
∆
∆
=
t
t
y
v
*2
•
Determine the Concept
The important concept here is that "average speed" is being
requested as opposed to "average velocity".
Under all circumstances, including
constant
acceleration
, the definition of the average
speed is the ratio of the total distance traveled (
H
+
H
) to the total time elapsed, in this
case 2
H
/
T
.
correct.
is
)
(
d
Remarks
:
Because this motion involves a round trip, if the question asked for
"average velocity," the answer would be zero.
3
•
Determine the Concept
Flying with the wind, the speed of the plane relative to the
ground (
v
PG
) is the sum of the speed of the wind relative to the ground (
v
WG
) and the
speed of the plane relative to the air (
v
PG
=
v
WG
+
v
PA
). Flying into or against the wind the
speed relative to the ground is the difference between the wind speed and the true air
speed of the plane
(
v
g
=
v
w
–
v
t
).
Because the ground speed landing against the wind is
smaller than the ground speed landing with the wind, it is safer to land
against
the wind.
4
•
Determine the Concept
The important concept here is that
a
=
dv/dt,
where
a
is the
acceleration and
v
is the velocity.
Thus, the acceleration is positive if
dv
is positive; the
acceleration is negative if
dv
is negative.
(
a
) Let’s take the direction a car is
moving to be the positive direction:
Because the car is moving in the direction
we’ve chosen to be positive, its velocity is
positive (
dx
> 0). If the car is braking, then
its velocity is decreasing (
dv
< 0) and its
acceleration (
dv
/
dt
) is negative.
(
b
) Consider a car that is moving to
Because the car is moving in the direction
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34
the right but choose the positive
direction to be to the left:
opposite to that we’ve chosen to be
positive, its velocity is negative (
dx
< 0). If
the car is braking, then its velocity is
increasing (
dv
> 0) and its acceleration
(
dv
/
dt
) is positive.
*5
•
Determine the Concept
The important concept is that when both the acceleration and
the velocity are in the same direction, the speed increases.
On the other hand, when the
acceleration and the velocity are in opposite directions, the speed decreases.
(
a
)
.
be
must
nt
displaceme
your
negative,
remains
ity
your veloc
Because
negative
(
b
)
reached.
is
wall
the
until
walking,
of
speed
the
slow
gradually
steps
five
last
the
During
direction.
negative
the
as
your trip
of
direction
the
Define
(
c
) A graph of
v
as a function of
t
that is consistent with the conditions
stated in the problem is shown to the
right:
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
t
(s)
v
(m/s)
6
•
Determine the Concept
True. We can use the definition of average velocity to express
the displacement
∆
x
as
∆
x = v
av
∆
t
. Note that, if the acceleration is constant, the average
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 Spring '07
 Licini

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