Vertical motion:
1. When a body is dropped from a height under gravity and neglecting the resistive forces, then, initial velocity of the body (u) is zero. The acceleration of the body is a = g.
The velocity of the body at time t is v = gt [using v = u + at].
The distance travelled by the body for time t is h = 
[using 
].
The velocity of the body when h height is travelled v = 
[using v2 = u2 + 2as].
2. When a body is thrown vertical upward with initial velocity u under gravitational acceleration g, then its final velocity is zero and it travels a maximum height H.
The velocity of the body at time t is v = u – gt [using v = u + at and a = – g].
The distance travelled by the body for time t is h = ut –  [using  and a = – g].
The velocity of the body when h height is travelled 
[using v2 = u2 + 2as and a = – g].
The maximum height travelled by the body is H = 
 [using v2 = u2 + 2as where v = 0 and a = – g].
Time of ascent and time of descent are same: A body is projected vertically upwards with velocity u and after time t it reaches the maximum height H before stop. Then using the equation v = u – gt we get, 0 = u – gt or, t = 
.
When the body is at height H then using the equation v2 = u2 – 2gH
We get, 0 = u2 – 2gH or, H = .
If the body takes time T to reach the ground from maximum height, then using the equation
Or, H = 0.T + 
Or, =
Or, T = .
So, Time of ascent = time of descent.