kinematics, t0 is zero

  • With a(t)=aa(t) = a, v(t0)=v0v(t_0) = v_0, x(t0)=x0x(t_0) = x_0, t0≠0t_0 \ne 0, the equations are
    v(t)=v0+a(t−t0),(H1)\tag{H1} v(t) = v_0 + a(t - t_0), x(t)=x0+v0(t−t0)+12a(t−t0)2.(H2)\tag{H2} x(t) = x_0 + v_0 (t - t_0) + \tfrac12 a (t - t_0)^2.
  • Set t0=0t_0 = 0, that makes v(0)=v0v(0) = v_0, x(0)=x0x(0) = x_0, will turn them into
    v(t)=v0+at,(H3)\tag{H3} v(t) = v_0 + at, x(t)=x0+v0t+12at2.(H4)\tag{H4} x(t) = x_0 + v_0 t + \tfrac12 a t^2.