The given equation is used to determine the distance covered by an object which was initially at rest. within a time t travelling by an acceleration due to gravity.
What is acceleration ?
Acceleration of an object is the rate of change in its gravity. When an object is falling freely, the acceleration it have by the force of gravitation.
The equation connecting the distance travelled and with the initial velocity u and time t with acceleration a is:
y = ut + 1/2at²
here, a is acceleration and t be the time.
If the object were at rest initially, the initial velocity is zero
when u = 0
y becomes, Y = 1/2 at²