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Kendra Kilmer February 3, 2012
Section 3.8  Rates of Change in the Natural and Social Sciences
Example 1:
A particle moves according to a law of motion
s
=
f
(
t
) =
0
.
01
t
4
−
0
.
04
t
3
,
t
≥
0, where
t
is measured
in seconds and
s
in feet.
a) Find the velocity at time
t
.
b) What is the velocity after 2 seconds?
c) When is the particle at rest?
d) When is the particle moving in the positive direction?
e) Find the total distance traveled during the first 8 seconds.
f) Draw a diagram to illustrate the motion of the particle.
14
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Kendra Kilmer February 3, 2012
g) Find the acceleration at time
t
and after 3 seconds.
h) Graph the position, velocity, and acceleration functions for
t
≥
0.
i) When is the particle speeding up? When is it slowing down?
Example 2:
In each of the following determine when the particle is speeding up and when the particle is slowing
down.
a) The graph of the position function of a particle is given where
t
is measured in seconds.
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This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.
 Fall '08
 Allen

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