What is free fall? Write the equations of uniformly accelerated motion for an object falling freely.

(N/A) The motion of an object falling solely under the influence of gravitational force is called free fall.
In this motion,the acceleration produced is the acceleration due to gravity $(g)$,which acts in the downward direction.
If air resistance is neglected,the motion is considered uniformly accelerated with acceleration $a = -g$.
By substituting the initial velocity $v_{0} = 0$,acceleration $a = -g$,and displacement $d = -h$ into the standard kinematic equations,we get:
$1$. For velocity: $v = v_{0} + at \implies v = -gt$
$2$. For displacement: $d = v_{0}t + \frac{1}{2}at^{2} \implies -h = 0 - \frac{1}{2}gt^{2} \implies h = \frac{1}{2}gt^{2}$
$3$. For velocity-displacement relation: $v^{2} - v_{0}^{2} = 2ad \implies v^{2} - 0 = 2(-g)(-h) \implies v^{2} = 2gh \implies v = \sqrt{2gh}$