Question text A mountain climber is steadily descending at -1.94 m/s using a rope. (Assume the positive direction is upward.) While going down...

Since, the climber is descending at a constant velocity, the first aid kit also has the same initial velocity. 

Thus, initial velocity of the first aid kit, u = -1.94 m/s (positive direction is upwards, by convention)

The time elapsed is, t = 3.7 s and the kit is falling downwards accelerating at 9.81 m/s^2 (in the downwards direction)

Using the equation of motion, 

s = ut + 1/2 at^2 = ut - 1/2 gt^2

= (-1.94) x 3.7 - 1/2 (9.81) (3.7)^2 = - 74.33 m

Thus, the medical kit has traveled a distance of 74.33 m in the downwards direction, after it accidentally fell out of climber's bag.

If the climber was stationary, the initial velocity would have been zero for the kit. If the climber was ascending, the initial velocity of the kit would have been positive and our answers would have been different.

Hope this helps.