$1.$ The distance between the two stations is $1\mathrm{.}6$ kms and the average speed of the train is $40$ kmph$,$ the acceleration, retardation during coasting and braking are $2$ km$/$h$/$s$,0\mathrm{.}16$ kmphps$,$ and $3\mathrm{.}2$ km$/$h$/$s respectively. Assume quadrilateral approximation of the speed time curve; determine the duration of the acceleration, coasting, and braking periods and distance covered during these periods.

$2.$ An electric train weighing $400$ tonnes running along an up gradient of $1\%$ with the following speed time curve: $($i$)$ uniform acceleration of $1\mathrm{.}5$ km$/$h$/$s for $30$ sec $($ii$)$ free running for $36$ sec $($iii$)$ coasting for $25$ sec $($iv$)$ braking at $2\mathrm{.}6$ km$/$h$/$s to rest. If tractive resistance is $45$N$/$tonne$,$ rotational inertia effect $10\%,$ overall efficiency of the transmission and motor is $75\%.$ Determine the specific energy consumption.

$3.$ Discuss the various methods of speed control of industrial drives. Write typical examples for each drive.