pokharel (yp624) – HW07 – Radin – (56520)
1
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13
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001
10.0 points
A storm system is headed towards Austin.
The Weather Service Office forecasts that
t
hours after midday the storm will be at a
distance of
s
(
t
) = 4 + 3
t

t
2
miles from Austin.
At what speed (in miles
per hour) will the storm be moving when it
reaches Austin?
1.
storm speed =

5 mph
2.
storm speed = 6 mph
3.
storm speed = 5 mph
correct
4.
storm speed =

7 mph
5.
storm speed = 7 mph
6.
storm speed =

6 mph
Explanation:
The storm will reach Austin when
s
(
t
) = (4

t
)(1 +
t
) = 0
,
i.e.
, when
t
= 4.
Now the velocity of the
storm is given by
s
′
(
t
) = 3

2
t,
the negative sign indicating that the storm is
moving towards Austin. Thus at
t
= 4,
s
′
parenleftBig
4
parenrightBig
= 3

8 =

5
.
Consequently,
since
speed
is
always
non
negative,
storm speed = 5 mph
.
002
10.0 points
If a rock is thrown vertically upwards from
the surface of the planet Newton with an
initial velocity of 7 ft/sec, its height after
t
seconds is given by
h
= 7
t

1
2
t
2
.
Find the velocity of the stone after it has risen
20 feet.
1.
velocity = 2 ft/sec
2.
velocity = 3 ft/sec
correct
3.
velocity = 1 ft/sec
4.
velocity = 0 ft/sec
5.
velocity = 4 ft/sec
Explanation:
When the height
h
= 20, then
20 = 7
t

1
2
t
2
.
After simplification and factorization this be
comes
t
2

14
t
+ 40 = (
t

4)(
t

10) = 0
.
Thus the rock will have risen 20 feet after 4
seconds. But its velocity is given by
dh
dt
= 7

t .
Consequently, after 4 seconds,
velocity = 3 ft/sec
.
003
10.0 points
Find the rate at which the volume of a
sphere is changing with respect to its radius
r
when
r
= 4 cm.
1.
rate = 24
π
cm
3
/
cm
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pokharel (yp624) – HW07 – Radin – (56520)
2
2.
rate = 36 cm
3
/
cm
3.
rate = 64
π
cm
3
/
cm
correct
4.
rate = 6 cm
3
/
cm
5.
rate = 48 cm
3
/
cm
Explanation:
For a sphere with radius
r
its
volume =
4
3
πr
3
.
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 Spring '10
 TSOI
 Acceleration, Velocity, RLM

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