55
Chapter 2
Motion in One Dimension
Conceptual Problems
1
•
What is the average velocity over the
″
round trip
″
of an object that is
launched straight up from the ground and falls straight back down to the ground?
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
Δ
Δ
=
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
Δ
0
Δ
Δ
av
=
=
=
t
t
y
v
2
•
An object thrown straight up falls back and is caught at the same place it
is launched from. Its time of flight is
T
, its maximum height is
H
. Neglect air
resistance. The correct expression for its average speed for the entire flight is
(
a
)
H
/
T
, (
b
) 0, (
c
)
H
/(2
T
), and (
d
) 2
H
/
T
.
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 elapsed
time, in this case 2
H
/
T
.
)
(
d
is correct.
Remarks
:
Because this motion involves a round trip, if the question asked for
"average velocity," the answer would be zero.
3
•
Using the information in the previous question, what is its average speed
just for the first half of the trip? What is its average velocity for the second half of
the trip? (Answer in terms of
H
and
T
.)
Determine the Concept
Under all circumstances, including
constant
acceleration
, the definition of the average speed is the ratio of the total distance
traveled to the elapsed time. The average velocity, on the other hand, is the ratio
of the displacement to the elapsed time.

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