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white (taw933) – HW07 – benzvi – (55600)
1
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001 (part 1 of 2) 10.0 points
It took Anna From noon until 3 p.m. to
drive From UT to her home 90 miles From
Austin. AFter
t
hours oF driving her distance
From Austin was given in miles by
s
(
t
) = 30
t
2

20
3
t
3
.
(i) What was her average speed For the trip
home?
1.
average speed = 29 mph
2.
average speed = 30 mph
correct
3.
average speed = 31 mph
4.
average speed = 32 mph
5.
average speed = 28 mph
Explanation:
Since Anna travelled 90 miles in 3 hours,
her
average speed = 30 mph
.
002 (part 2 of 2) 10.0 points
(ii) Her instantaneous speed twice coincided
with her average speed. At what time did
it frst happen?
1.
at 12:37 pm
correct
2.
at 12:47 pm
3.
at 12:42 pm
4.
at 2:21 pm
5.
at 2:31 pm
Explanation:
Anna’s instantaneous speed at time
t
was
was
s
′
(
t
) = 60
t

20
t
2
,
and this would coincide with her average
speed when
60
t

20
t
2
= 30
,
i.e.
, when
t
2

3
t
+
3
2
= 0
.
The quadratic Formula gives solutions
t
=
1
2
p
3
±
√
9

6
P
=
p
√
3
±
1
2
√
3
P
3
.
Both solutions are positive, so we need only
the smaller solution. But as a decimal
p
√
3

1
2
√
3
P
3
≈
0
.
633
.
Consequently, Anna’s instantaneous speed
frst coincided with her average speed For the
trip
at 12:37 pm
.
003
10.0 points
A storm system is in the Central Texas area
and moving in a straight line through Austin.
The Weather Service O±ce Forecasts that
t
hours aFter 12noon the the storm will be a
distance oF
s
(
t
) = 24 + 2
t

t
2
miles From Austin. How Fast will the storm be
moving at 4:00 pm and in what direction will
it be moving?
1.
storm speed = 8 mph,
storm moving
towards Austin.
2.
storm speed = 6 mph,
storm moving
away From Austin.
3.
storm speed =

6 mph,
storm moving
towards Austin.
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View Full Documentwhite (taw933) – HW07 – benzvi – (55600)
2
4.
storm speed =

8 mph,
storm moving
towards Austin.
5.
storm speed = 8 mph,
storm moving
away from Austin.
6.
storm speed = 6 mph,
storm moving
towards Austin.
correct
Explanation:
Since
s
(
t
) =

(
t
+ 4)(
t

6)
,
the storm will pass through Austin at 6:00
pm. Now
t
hours after 12noon the velocity of
the storm will be given by
s
′
(
t
) = 2

2
t.
Thus at 4:00 pm,
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 Spring '08
 schultz
 Differential Calculus

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