11 Nov 2021
Problem 57a
Page 323
Section 4.8: Antiderivatives
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
11 Nov 2021
Given information
A high-speed bullet train accelerates and decelerates at the rate of 
. Its maximum cruising speed is 
.
The train accelerates from rest until it reaches its cruising speed and then runs at that speed for 
minutes.
Step-by-step explanation
Step 1.
We know that speed 
is the antiderivative of acceleration 
.
Therefore
Therefore
where 
is the initial velocity and represents the arbitrary constant.
We have here 
Therefore 
Now distance traversed 
is the antiderivative of velocity .
Therefore 
.
Therefore 
Therefore 
where 
is the arbitrary constant.
We know that at 
; 
Therefore on substitution in the equation above we have 
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
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- Problem 38
- Problem 39
- Problem 40a
- Problem 40b
- Problem 40c
- Problem 40d
- Problem 41
- Problem 42
- Problem 43a
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- Problem 43c
- Problem 43d
- Problem 44
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- Problem 48
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- Problem 53
- Problem 54a
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- Problem 55a
- Problem 55b
- Problem 55b
- Problem 56
- Problem 57a
- Problem 57b
- Problem 57c
- Problem 57d
- Problem 58a
- Problem 58b
- Problem 58c