Free-fall: Discuss the motion of an object under free fall. Neglect air resistance.

(N/A) An object released near the surface of the Earth is accelerated downward under the influence of the force of gravity. The magnitude of acceleration due to gravity is represented by $g$. If air resistance is neglected,the object is said to be in free fall. If the height through which the object falls is small compared to the Earth's radius,$g$ can be taken to be constant,equal to $9.8 \ m \ s^{-2}$. Free fall is thus a case of motion with uniform acceleration.
We assume that the motion is in $y$-direction,more correctly in $-y$-direction because we choose the upward direction as positive. Since the acceleration due to gravity is always downward,it is in the negative direction and we have $a = -g = -9.8 \ m \ s^{-2}$.
The object is released from rest at $y = 0$. Therefore,$v_0 = 0$ and the equations of motion become:
$v = 0 - gt = -9.8t \ m \ s^{-1}$
$y = 0 - 1/2 gt^2 = -4.9t^2 \ m$
$v^2 = 0 - 2gy = -19.6y \ m^2 \ s^{-2}$
These equations give the velocity and the distance travelled as a function of time and also the variation of velocity with distance. The variation of acceleration,velocity,and distance with time are shown in the figures.