Problem 57b
Page 323
Section 4.8: Antiderivatives
Chapter 4: Applications of Differentiation
Given information
A high-speed bullet train accelerates and decelerates at the rate of 
. Its maximum cruising speed is 
.
The train starts from rest and must come to a complete stop in 
minutes.
Step-by-step explanation
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 for 
bbefore coming to a stop.
Therefore the train cruises for 
at a uniform speed of 
thus travelling a distance of 
Therefore the maximum distance the train covers in is 
Single Variable Calculus: Early Transcendentals
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