2'2 Rates of change cont'

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2.2 Rates of change cont.

• "The shortest distance between two points is
  under construction." -- Bill Sanderson

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Objective

• To find instantaneous velocity and acceleration

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Rates of change

• Population growth rates
• Production rates
• Water flow rates
• Velocity
• Acceleration
• Others????

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Review

• Rate distance/time
• s(t) position function
• Average velocity

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Average Velocity

• If a billards ball is dropped from a height of
  100 feet, given by the function
• Find the average velocity of the intervals 1, 2
  1 1.5 1, 1.1

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Question

• What about instantaneous velocity, or the
  velocity of an object at exactly one minute?

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Instantaneous Velocity

• Equation
• Velocity can be positive (going up), negative
  (going down), or zero
• Speed is always positive absolute value of
  velocity

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Ex 10, pg 109
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Position equation

• A football is thrown upwards from the top of a 30
  ft house with an initial velocity of 15 ft/sec.
  What is the velocity after 1 second? What is the
  velocity when it hits the ground?

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Example cont

• A football is thrown upwards from the top of a 30
  ft house with an initial velocity of 15 ft/sec.
  What is the velocity after 1 second? What is the
  velocity when it hits the ground?