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20.
Picture the Problem
: You travel in a straight line at two different speeds during the specified time interval.
Strategy:
Determine the average speed by first calculating the total distance traveled and then dividing it by
the total time elapsed.
Solution:
1. (a)
Because the time intervals are the same, you spend equal times at 20 m/s and 30 m/s, and your
average speed will be equal to 25.0 m/s.
2.
(b)
Divide the total distance
by the time elapsed:
(
29
(
29
(
29
(
29
1
1
2
2
av
1
2
av
20.0 m/s 10.0 min 60 s
30.0 m/s
600 s
600
600 s
25.0 m/s
s
t
s
t
s
t
t
s
×
+
∆ +
∆
=
=
∆ + ∆
+
=
Insight:
The average speed is a weighted average according to how much
time
you spend traveling at each
speed.
25.
Picture the Problem
: The given position function indicates the particle begins traveling in the positive
direction but is accelerating in the negative direction.
Strategy:
Create the
x

versus

t
plot using a spreadsheet, or calculate individual values by hand and sketch the
curve using graph paper.
Use the known
x
and
t
information to determine the average speed and velocity.
Solution:
1. (a)
Use a spreadsheet to create the plot shown at right:
2.
(b)
Find the average velocity
from
t
= 0 to
t
= 1.0 s:
(
29
(
29
(
29
(
29
[
]
av
2
2
av
6 m/s 1.0 s
2 m/s
1.0 s
0.0 m
1.0 s
4.0 m/s
x
v
t
v
∆
=
∆
+ 

=
=
3.
(c)
The average speed is the
magnitude of the average velocity:
av
av
4.0 m/s
s
v
=
=
Insight:
Note that the average velocity over the first second of time is equal to the slope of a straight line
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 Spring '11
 BEAN
 pH

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