3.4
Velocity
and
Other
Rates
of
Change
Instantaneous Rate of Change
f
¢
H
a
L
=
lim
h
Æ
0
f
H
a
+
h
L

f
H
a
L
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
h
Velocity, Speed, and Acceleration
If the position function is described by s
H
t
L
, then
velocity
=
v
H
t
L
=
s
¢
H
t
L
speed
=
»
v
H
t
L »
=
»
s
¢
H
t
L »
acceleration
=
a
H
t
L
=
v
¢
H
t
L
=
s
¢¢
H
t
L
Free

fall Constants on Earth
English units
Æ
s
= 
16t
2
a
= 
32
ft
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
sec
2
Metric units
Æ
s
= 
4.9t
2
a
= 
9.8
m
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
sec
2
Marginal Cost
Marginal Cost is the derivative of the Cost function.
1.
A
particle
moves
along
a
line
so
that
its
position
at
any
time
t
≥
0
is
given
by
s
H
t
L
=
t
2

t

4,
where s is
measured in meters and t is measured in seconds.
Find
H
a
L
the displacement in the first 3 seconds
H
b
L
the average velocity in the first 3 seconds
H
c
L
the acceleration at t
=
3 seconds
H
d
L
where the particle is when
s is a minimum
H
e
L
the velocity when
t
=
3 seconds
H
a
L
s
H
3
L

s
H
0
L
=
2

H

4
L
=
6 meters
H
b
L
average velocity
=
6 meters
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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 Spring '08
 GREENE
 Calculus, Derivative, Rate Of Change, Velocity, HtL, ÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄ

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