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Calculus Section 3.4
Page19
3.4
Velocity and Other Rates of Change
Remember
slope of secant line
slope of tangent line
(diagram)
Average velocity
=
distance traveled
total time
(assume you are going in one direction)
What is this like?
Suppose you drive your car for 2 h and travel exactly 80 mi.
What is your
average
velocity
?
Instantaneous velocity
= first derivative of the distance function = s'(t) =
ds
dt
What is this like?
In the Calculus AP course, we are just concerned with rectilinear motion (motion of a
particle along a line)
Summary
s(t)
gives position
s'(t) =0 ___________
s'(t)
gives velocity
s'(t) > 0___________
s'(t) < 0___________
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View Full DocumentCalculus Section 3.4
Page 20
Example 1
s(t) = t
3
– 6t
2
+ 9t
(t is measured in sec, s is measured in ft)
a)
find the velocity at time t
b)
what is the velocity after 2 sec,
after 4 sec?
c)
when is the particle at rest?
d)
when is the particle moving to the right (in a positive direction)?
e)
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 Spring '10
 John
 Calculus, Slope

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