These equations relate displacement, velocity, acceleration, and time, and apply for constant acceleration in the +x direction starting at t=0.

v = v_o + at (1)

x = x_o + v_o t + ½ a t² (2)

Using Eq. (1), at = v - v_o, in Eq. (2), we get:

x = x_o + v_o t + ½ (v - v_o) t

=x_o + ½ (v + v_o) t (3)

= x_o + v_av t

Rearranging (1), t = (v- v_o)/a, and substituting for t in (3) gives:

x = x_o +½(v + v_o) (v- v_o)/a or 2 a (x - x_o)= v² - v_o² (4)

Eqs. (1) - (4) are the basic equations of kinematics that relate acceleration, velocity, and displacement.