Question $1$

A pit shaft is $500$ m deep and the cage is raised at a maximum velocity of $16$ m$/$s$.$ If the speed attained $5$ seconds from res, and the cage is brought uniformly to rest in the last $25$ m of travel, determine using a velocity$/$time graph:$-$

$*$ the acceleration and the distance travelled during acceleration

$*$ the retardation and the time taken to come to rest

$*$ The total travel time

Question $2$ Two stations are $3\mathrm{.}6$ km apart and the running time of a train between them is $5$ minutes. If acceleration occurs during the first $1\mathrm{.}5$ minutes and the retardation in the last minute with constant speed in the intervening time, determine :$-$

$*$ the maximum speed attained.

$*$ the acceleration and the corresponding distance travelled.

$*$ the retardation and the distance travelled during that time.

Question $3$

A rocket leaves its pad vertically with an acceleration of $7\mathrm{.}5$ m$/$s$^2$ which remains constant until the fuel is exhausted after $8$ seconds. It then continues to travel freely in the vertical direction. Find the total time taken for the rocket to reach its highest point and the altitude achieved.