v = u + at
This is the simplest equation. It can be used when displacement is not given, but if 3 variables among initial velocity, final velocity , acceleration and time are given.
s = ut + ½at²
This equation is most commonly used to solve problems involving falling objects.
s = ½ (u+v) t
This equation is used if acceleration is not known.
v² = u² + 2as
This equation is used when time is not given.
v = final velocity
u = initial velocity
a = acceleration
t = time taken
s = displacement
Here is a simple explanation of how the above equations have been derived from velocity-time graphs using algebra.
For detailed explanations , motion graphs & problem solving, go to the physics classroom.