Velo
Position $$\tag{D3} x(t) = \left\{ \begin{array}{cc} x_0 + v_0(t - t_0) + \tfrac12 a_0(t - t_0)^2, & t_0 \le t < t_1, \\[0.5em] x_1 + v_1(t - t_1) + \tfrac12 a_1(t - t_1)^2, & t_1 \le t < t_2, \end{array} \right. $$ with $t_{n+1} = t_n + \tau_n$, where $\tau_n$ is $n$-th time interval. Initial conditions $x(t_0) = x_0$, $x(t_1) = x_1$ and $x(t_1) = x_0 + v_0(t_1 - t_0) + \tfrac12 a_0(t_1 - t_0)^2$.Velocity $$\tag{D2} v(t) = \left\{ \begin{array}{cc} v_0 + a_0(t - t_0), & t_0 \le t < t_1, \\[0.5em] v_1 + a_1(t - t_1), & t_1 \le t < t_2, \end{array} \right. $$ with $t_{n+1} = t_n + \tau_n$, where $\tau_n$ is $n$-th time interval. Initial conditions $v(t_0) = v_0$, $v(t_1) = v_1$ and $v(t_1) = v_0 + a_0(t_1 - t_0)$.Acceleration $$\tag{D1} a(t) = \left\{ \begin{array}{cc} a_0, & t_0 \le t < t_1, \\[0.5em] a_1, & t_1 \le t < t_2, \end{array} \right. $$ with $t_{n+1} = t_n + \tau_n$, where $\tau_n$ is $n$-th time interval.Acceleration $$\tag{C1} a(t) = a_n, \ \ \ \ t_n < t < t_{n+1}. $$ Velocity $$\tag{C2} v(t) = v_n + a_n(t - t_n), \ \ \ \ t_n \le t \le t_{n+1}. $$ Posisition $$\tag{C3} x(t) = x_n + v_n(t - t_n) + \tfrac12 a_n(t - t_n)^2, \ \ \ \ t_n \le t \le t_{n+1}. $$Velocity $$\tag{B1} v(t) = v_n + a(t - t_n), \ \ \ \ t_n \le t \le t_{n+1}. $$ Initial condition $$\tag{B2} x(t_n) = x_n. $$ Posisition $$\tag{B3} x(t) = x_n + v_n(t - t_n) + \tfrac12 a_n(t - t_n)^2, \ \ \ \ t_n \le t \le t_{n+1}. $$Constant acceleration $$\tag{A1} a(t) = a_n, \ \ \ \ t_n < t < t_{n+1}. $$ Initial condition $$\tag{A2} v(t_n) = v_n. $$ Velocity $$\tag{A3} v(t) = v_n + a_n(t - t_n), \ \ \ \ t_n \le t \le t_{n+1}. $$