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The Concept of
AVERAGE RATE OF
CHANGE
SPEED
Suppose we are tracking Barney as he falls from the Sears Tower. To find the average speed
Barney is falling over any particular time interval, divide the amount of distance covered during
the time interval by the length of the time interval. Since Barney is falling freely near the surface
of the earth, then his position can be calculated with the equation y = 16t
2
ft. To find his average
speed for the first 10 seconds, we will find
∆
y/
∆
t.
y
x
=
16
10
2
−
16
0
2
10
−
0
=
1600
−
0
10
=
160
ft
/
sec
If we want to find Barney's average speed during a 1second interval between 12 and 13 seconds,
then the average speed will have the following form.
y
x
=
16
13
2
−
16
12
2
13
−
12
=
2704
−
2304
1
=
400
ft
/
sec
Suppose we want to find Barney's generic speed as he travels from t
0
to t
0
+ h. Barney's average
speed will be
y
x
=
16
t
0
h
2
−
16
t
0
2
t
0
h
−
t
0
=
16
t
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 Spring '08
 Noohi
 Rate Of Change

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