myers (nmm698) – HW02 – Hamrick – (54868)
1
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001
10.0 points
A tank holds 1000 gallons of water, which
drains from the bottom of the tank in half an
hour. The values in the table
t
(min)
5
10
15
20
25
30
V
(gal)
656
420
292
147
16
0
show the volume,
V
(
t
), of water remaining in
the tank (in gallons) after
t
minutes.
If
P
is the point (15
, V
(15)) on the graph
of
V
as a function of time
t
, find the slope of
the secant line
PQ
when
Q
= (25
, V
(25)).
1.
slope =
−
14
.
5
2.
slope =
−
36
.
4
3.
slope =
−
12
.
8
4.
slope =
−
27
.
6
correct
5.
slope =
−
55
.
2
Explanation:
When
P
= (15
, V
(15))
,
Q
= (25
, V
(25))
the slope of the secant line
PQ
is given by
rise
run
=
V
(25)
−
V
(15)
25
−
15
.
From the table of values, therefore, we see
that
slope =
16
−
292
25
−
15
=
−
27
.
6
.
002
10.0 points
The position of a car as a function of time
is given by the values in table
t
(seconds)
0
1
2
3
4
5
s
(feet)
0
14
22
28
46
58
Find the average velocity for the time period
beginning when
t
= 2 and lasting 2 seconds.
1.
average vel. = 12 feet/sec
correct
2.
average vel. = 13 feet/sec
3.
average vel. = 14 feet/sec
4.
average vel. = 16 feet/sec
5.
average vel. = 15 feet/sec
Explanation:
Average velocity between times
t
= 2 and
t
= 2 +
h
is given by
dist. travelled
time taken
=
s
(2 +
h
)
−
s
(2)
h
.
When
h
= 2, therefore,
s
(2 + 2)
−
s
(2)
2
=
s
(4)
−
s
(2)
2
=
46
−
22
2
.
Consequently, over the time interval from
t
=
2 to
t
= 4 the car has
average velocity = 12 ft/sec
.
003
10.0 points
A car is driven at a constant speed. Sketch
a graph of the position of the car as a function
of time.
1.
time
position
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myers (nmm698) – HW02 – Hamrick – (54868)
2
2.
time
position
3.
time
position
4.
time
position
5.
time
position
6.
time
position
correct
Explanation:
When the position of the car is plotted
against time, the slope of the graph indicates
the speed of the car, the greater the slope, the
greater the speed, and the car is stationary
when the slope is zero.
Thus of the graphs,
only
time
position
has the given properties.
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 Fall '08
 schultz
 Derivative, Slope, average vel

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