These equations relate displacement, velocity, acceleration, and time, and apply under the following conditions:

the acceleration is constant
the motion is measured from t = 0
the fact that several variables are vectors is accounted for with appropriate plus and minus signs

v = v_o + at

x - x_o = v_o t + ½ a t²

x - x_o = ½ (v + v_o) t

v² = v_o² + 2 a (x - x_o)

The equations are derived from the definitions of acceleration, velocity, and displacement.