69. Suppose you throw a ball straight up into the air at a velocity of vo = 42 feet per second, initially releasing the ball at a height of 4 feet. Acceleration due to gravity is constantly a(t) = –32 feet per second squared (negative since it pulls downward). Position, velocity, and acceleration of a ball thrown upwards 42 t 2.5 0.5 -32 (a) Calculate ſ a(t) dt. Then, given that acceleration is the derivative of velocity and that the initial velocity was vo = 42, find a formula for the velocity v(t) of the ball after t seconds. (b) Calculate ſv(t) dt. Then, given that velocity is the derivative of position and that the initial position was So = 4 feet, find a formula for the velocity s(t) of the ball after t seconds. (c) Discuss the relationships among the graphs of s(t), v(t), and a(t) shown in this exercise.
69. Suppose you throw a ball straight up into the air at a velocity of vo = 42 feet per second, initially releasing the ball at a height of 4 feet. Acceleration due to gravity is constantly a(t) = –32 feet per second squared (negative since it pulls downward). Position, velocity, and acceleration of a ball thrown upwards 42 t 2.5 0.5 -32 (a) Calculate ſ a(t) dt. Then, given that acceleration is the derivative of velocity and that the initial velocity was vo = 42, find a formula for the velocity v(t) of the ball after t seconds. (b) Calculate ſv(t) dt. Then, given that velocity is the derivative of position and that the initial position was So = 4 feet, find a formula for the velocity s(t) of the ball after t seconds. (c) Discuss the relationships among the graphs of s(t), v(t), and a(t) shown in this exercise.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:69. Suppose you throw a ball straight up into the air at a
velocity of vo = 42 feet per second, initially releasing the
ball at a height of 4 feet. Acceleration due to gravity is
constantly a(t) = –32 feet per second squared (negative
since it pulls downward).
Position, velocity, and acceleration
of a ball thrown upwards
42
t
2.5
0.5
-32
(a) Calculate ſ a(t) dt. Then, given that acceleration is the
derivative of velocity and that the initial velocity was
vo = 42, find a formula for the velocity v(t) of the ball
after t seconds.
(b) Calculate ſv(t) dt. Then, given that velocity is the
derivative of position and that the initial position was
So = 4 feet, find a formula for the velocity s(t) of the
ball after t seconds.
(c) Discuss the relationships among the graphs of s(t),
v(t), and a(t) shown in this exercise.
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