Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 38

(a) If the maximum acceleration that is tolerable for passengers in a subway train is $1.34 \text{ m/s}^2$ and subway stations are located $806 \text{ m}$ apart, what is the maximum speed a subway train can attain between stations? (b) What is the travel time between stations? (c) If a subway train stops for $20 \text{ s}$ at each station, what is the maximum average speed of the train, from one start-up to the next? (d) Graph $x$, $v$, and $a$ versus $t$ for the interval from one start-up to the next.