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Unformatted text preview: Lecture 19: Rates of Change Applications (Chapter 3, Section 19) Recall the following: Average Rate of Change 6 ? Instantaneous Rate of Change If s = f ( t ) is the position of a particle moving in a straight line, then 2 ex. Suppose the position of a particle is given by s = f ( t ) = 2 t 3 ¡ 15 t 2 + 24 t where t is measured in seconds and s in feet. a) Find the velocity of the particle at any time t . b) Find the velocity at t = 1 2 and t = 2 seconds. c) When is the particle at rest? 3 d) When is the particle moving in a positive direc tion? e) Draw a diagram to represent the motion of the particle. f) Find the total distance moved in the flrst flve sec onds. 4 Acceleration g) Find the acceleration of s ( t ) = 2 t 3 ¡ 15 t 2 +24 t at any time t . h) When is the object speeding up and when is it slowing down? 5 ex. A dynamite blast blows a small boulder straight up with a velocity of 160 ft/sec. Its height at any time t is f ( t ) = 160 t ¡ 16 t 2 . a) Find its velocity at any time t . b) What is the boulder’s maximum height? c) What is the velocity and speed when it is 256 ft above ground (on its way up and on the way down). 6 d) What is the acceleration of the boulder at any time? When is it slowing down and speeding up?...
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 Spring '08
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 Calculus, Geometry, Rate Of Change

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