Consider an object moving with uniform acceleration, a. Let u be the initial velocity (at time t = 0), v, velocity after time t and S, displacement during this time interval. There are certain relationships between these quantities.
Acceleration = Change in velocity / Time interval
a = (v - u)/t
v = u + at
This is called as the first equation of motion.
Displacement = (average velocity) × (time interval)
s = (v + u)/2 × t
s = (u + at + u)/2 × t
s = ut + ½at2
This is called the second equation of motion.
If object starts from rest, u = 0
s = ½at2
Thus, the displacement of an object undergoing a constant acceleration is proportional to t2, while the displacement of an object with constant velocity (zero acceleration) is proportional to t.
a = (v - u)/t and s = (v + u)/2 × t
a.s = (v2 - u2)/2
v2 = u2 + 2as
This is called as third equation of motion. In case of motion under gravity a can be replaced by g.