Rates of Change and the Slope of a Curve

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Rates of Change and the Slope of a Curve
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Imagine a dragster
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• A dragster can cover ¼ mile track (402 m ) in
  about 4.5 seconds
• That is CDCI WEST to King and Division

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Think back to distance vs time graphsSuppose a
dragster can cover 402m in 4.5 seconds

• D(m)

4.5
402 0
402
0 1 2 3 4 5
t(s)
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• This is a calculation of the average speed of the
  dragster.
• We know in reality, the cars speed is not
  constant. The car actually accelerates from zero,
  to its top speed at the end of the course.
• A true distance time graph of this will be curved

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An average speed can be calculated by using the
two endpoints

• D(m)

(4.5, 402)
402 0
This is called the average rate of change
(0,0)
0 1 2 3 4 5
T(s)
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What if we wanted to know the speed of the
dragster after 3 seconds(This is called the
instantaneous rate of change)this is big
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An average speed can be calculated by using 2
points

• D(m)

(4.5,402)
secant
402 0
What if we moved that second point closer?...
(3, 50)
0 1 2 3 4 5
T(s)
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We are now going to complete an investigation
from 1.1
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Homework

• See homework sheet 1-9

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Calculation of the slope