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92.131
Lecture 7
1 of 9
Ronald Brent © 2009 All rights reserved.
Average and Instantaneous Speed
A moving body’s average speed during a time interval is defined as the
distance covered divided by the elapsed time. As this time interval gets smaller
and smaller the value we approach is called the instantaneous speed.
Suppose
2
16
t
y
=
is the distance (in feet) an object has moved in a time
interval (in seconds), then computing the change in
y
(denoted
y
Δ
) and the time
elapsed (denoted
t
Δ
,) one can calculate the average velocity in that time
interval.
For example the average velocity in the first 2 seconds is
sec
/
ft
32
0
2
)
0
(
16
)
2
(
16
2
=
−
−
=
Δ
Δ
t
y
The average velocity during the 1 second interval between second 1 and second
2 is
sec
/
ft
48
1
2
)
1
(
16
)
2
(
16
2
=
−
−
=
Δ
Δ
t
y
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View Full Document 92.131
Lecture 7
2 of 9
Ronald Brent © 2009 All rights reserved.
By letting the time interval get smaller and smaller, we can define the
instantaneous velocity or a velocity at one point. Consider the time interval
]
,
[
0
0
h
t
t
+
, then the change in distance divided by the change in time is
h
t
h
t
t
y
2
0
2
0
)
(
16
)
(
16
−
+
=
Δ
Δ
Let’s compute the average speed at the time
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.
 Fall '09
 Staff
 Calculus

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