The acceleration due to gravity on planet X is one fifth of that on the surface of the Earth. If it takes 3.4 s for an object to fall a certain distance from rest on Earth, how long would it take for the object to fall the same distance on planet X? Answer in the units of s.

The equation of the fall from rest under the influence of only gravity is
x = g*t^2/2 , where x is the height of the fall, a is the acceleration due to gravity, and t is the time during which the fall took place. 
For the object on the surface of the Earth, acceleration due to gravity is g = 9.8 m/s^2 and the time t_E of the fall from rest is 3.4 s.
For the object on planet X, the acceleration due to gravity is g/5. Then, the time t_x of the fall from rest from the same height can be determined from
g (3.4)^2/2 = 1/2*g/5*t_x^2
From here,
t_x = sqrt(5)*3.4 s=7.6 s .
It would take sqrt(5)
times longer for the object to fall on the planet where the gravity is five times weaker.
On planet X, it would take the object 7.6 seconds to fall the same distance.
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html