kinematics equations summaries

There are three to five kinematics equations reported, where from the first two ( $v = v_0 + at$ and $x = x_0 + v_0 t + \tfrac12 at^2$ ), the third can be obtained, also the fourth and the fifth, by eliminating an unknown.
The idea of five equations is that each for one unknown, which are $x - x_0$ , $v$ (or $v_t)$ , $t$ (or $\Delta t$ , $t - t_0$ ), $v_0$ , and $a$ .
They are obtained by integration of constant acceleration $a$ and using initial conditions for velocity $v(t_0) = v_0$ and position $x(t_0) = x_0$ with $t_0 \ne 0$ in general, but it is common to choose $t_0 = 0$ .