Calc I Notes – Motion
Calc I Notes – Motion Wed, March 28 Name _________________
From the perspective of a physics student:
Position of a freely falling body s is given by [pic] where g is the acceleration due to gravity [pic], t is time in seconds, [pic] = initial velocity, and [pic] = initial position.
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Vocabulary:
[pic] = rate of change of position = [pic]
average velocity = [pic] (slope formula for average rate of change)
[pic] = [pic] [pic]
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ex 1 – Find the average velocity from t = 1 to t = 3 for [pic] (English system or metric system?)
ex 2 – Find the instantaneous velocity at t = 1.4 sec.
ex 3 – Do you think that instantaneous velocity could equal average velocity? If so, when?
ex 4 – At time t = 0, a diver jumps from a diving board 32 ft above water. This situation follows the
function [pic] Physics scholars: What does the first [pic] mean?___________
What does the second 16 mean? ____________ What does the 32 mean?_____________
(a) When does she hit the water?
(b) What is her velocity at impact?
(c) How long does it take to get to the highest point?
(d) What is that highest point?
(e) When is velocity negative?
(f) When is the diver exactly 33 ft above water? (Solve on GC.)
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velocity = [pic] acceleration = [pic] or [pic] (second derivative of position with respect to time)
ex 5 – A projectile is fired upwards from a ten foot platform with an initial velocity of 160 ft/sec. Find
the position function if t = 0 when the projectile is fired.
(Start with acceleration due to gravity and use “separation of variables.”)
[pic]
due Friday, Mar 30 – A*33 p.137 #19, 24; and
find the body’s position s at time t given that [pic]
Also, find the body’s position s at time t given that [pic]
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