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:In part a of Preview Activity 4.4.1 , what is the interpretation of s (0) = 32?
When the balloon starts its journey, it is thrown with an upwards velocity of 32 ft/sec.
When the balloon starts its journey, its height is 32 feet above ground.
When the balloon has been in flight for 32 seconds, it hits the ground (height 0).
![For instance, for the velocity function in Figure 4,4.1 , the total distance D
traveled by the moving object on [a, b] is
D= A1 + A2 + A3,
and the total change in the object's position is
s(b) – s(a) = A1 – A2 + A3.
The areas A1, A2, and Ag are each given by definite integrals, which may be
computed by limits of Riemann sums (and in special circumstances by geometric
formulas).
y = v(1)
A1
A3
A2
a
Figure 4.4.1. Avelocity function that is sometimes negative.
ANSWER THE QUESTION IN REGARDS TO THIS
We turn our attention to an alternate approach.
Preview Activity 4.4.1. A student with a third floor dormitory window 32
feet off the ground tosses a water balloon straight up in the air with an initial
velocity of 16 feet per second. It turns out that the instantaneous velocity of the
water balloon is given by v(t) = –32t + 16, where v is measured in feet per
second and t is measured in seconds.
a. Let s(t) represent the height of the water balloon above ground at time t,
and note that s is an antiderivative of v. That is, v is the derivative of s:
s'(t) = v(t). Find a formula for s(t) that satisfies the initial condition that
the balloon is tossed from 32 feet above ground. In other words, make
your formula for s satisfy s(0) = 32.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6df2ec1a-dffc-4a86-a267-06e40e227b92%2Ff3f799c9-6b15-4ee9-abf7-28e35ab3503e%2Fgwjg9d_processed.png&w=3840&q=75)
Transcribed Image Text:For instance, for the velocity function in Figure 4,4.1 , the total distance D
traveled by the moving object on [a, b] is
D= A1 + A2 + A3,
and the total change in the object's position is
s(b) – s(a) = A1 – A2 + A3.
The areas A1, A2, and Ag are each given by definite integrals, which may be
computed by limits of Riemann sums (and in special circumstances by geometric
formulas).
y = v(1)
A1
A3
A2
a
Figure 4.4.1. Avelocity function that is sometimes negative.
ANSWER THE QUESTION IN REGARDS TO THIS
We turn our attention to an alternate approach.
Preview Activity 4.4.1. A student with a third floor dormitory window 32
feet off the ground tosses a water balloon straight up in the air with an initial
velocity of 16 feet per second. It turns out that the instantaneous velocity of the
water balloon is given by v(t) = –32t + 16, where v is measured in feet per
second and t is measured in seconds.
a. Let s(t) represent the height of the water balloon above ground at time t,
and note that s is an antiderivative of v. That is, v is the derivative of s:
s'(t) = v(t). Find a formula for s(t) that satisfies the initial condition that
the balloon is tossed from 32 feet above ground. In other words, make
your formula for s satisfy s(0) = 32.
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