the 3rd kine eqns, p2

  • From previous equations following can be obtained $$\tag{I4} x = x_0 + v_0 \left( \frac{v - v_0}{a} \right) + \tfrac12 a \left( \frac{v - v_0}{a} \right)^2. $$
  • It can be simplified into $$\tag{I5} \begin{array}{rcl} 2a(x - x_0) & = & 2v_0 (v - v_0) + (v - v_0)^2 \newline & = & (2v_0 + v - v_0)(v - v_0) \newline & = & (v_0 + v)(v - v_0). \end{array} $$