A certain freely falling object, released from rest, requires $1\mathrm{.}75$ s to travel the last $36\mathrm{.}5$ m before it hits the ground.

$($a$)$ Find the velocity of the object when it is $36\mathrm{.}5$ m above the ground. $($Indicate the direction with the sign of your answer. Let the positive direction be upward.$)$

m$/$s

$($b$)$ Find the total distance the object travels during the fall.