11 Nov 2021
Problem 57c
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 
.
Distance between between two consecutive stations that are 
miles apart.
Step-by-step explanation
Step 1.
From 57(a) we have the following equation of dynamics for the train in acceleration on substitution 
The train reaches the maximum cruise speed 
in 
and decelerates to a complete stop in iin a similar manner.
We saw from 57(a) the train travels 
before reaching the cruise speed
Therefore it takes 
to accelerate upto cruise speed and decelerate to 0 and travels a total distance of 
during acceleration and deceleration.
The train has to travel 
from one station to other.
Therefore the train cruises for 
at a uniform speed of 
thus travelling for 
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
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