26. (a)
To graph the velocity, we estimate the slopes at several
points as follows, then connect the points to create a
smooth curve.
To graph the acceleration, we estimate the slope of the
velocity graph at several points as follows, and then
connect the points to create a smooth curve.
(b)
}
d
d
s
t
}
5
30
t
2
3
t
2
[0, 15] by [
2
300, 100]
}
d
dt
2
2
s
}
5
30
2
6
t
[0, 15] by [
2
100, 50]
The graphs are very similar.
27. (a)
Solving 160
5
490
t
2
gives
t
5 6
}
4
7
}
.
It took
}
4
7
}
of a second. The average velocity was
sec = 280 cm/sec.
(b)
v
5
s
9
(
t
)
5
980
t
a
5
s
0
(
t
)
5
980
The velocity was
s
9
1
}
4
7
}
2
5
560 cm/sec.
The acceleration was
s
0
1
}
4
7
}
2
5
980 cm/sec
2
.
(c)
Since there were about 16 flashes during
}
4
7
}
of a second,
the light was flashing at a rate of about 28 flashes per
second.
28.
Graph C is position, graph A is velocity, and graph B is
acceleration.
A is the derivative of C because it is positive, negative, and
zero where C is increasing, decreasing, and has horizontal
tangents, respectively. The relationship between B and A is
similar.
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 Fall '08
 GERMAN
 Slope, Velocity, dy, 160 cm, 980 cm, 280 cm, 560 cm

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