x = {{0.1},{0.2}};
Do[datax[i] = {}; dataxm[i] = {};, {i, 1, 2}]

Do[
 x = x + t;
 Do[AppendTo[datax[i], Flatten[{t, x[[i]]}]];, {i, 1, 2}], {t, 0, 1, 0.1}]


 datax[1]

 {{0., 0.1}, {0.1, 0.2}, {0.2, 0.4}, {0.3, 0.7}, {0.4, 1.1}, {0.5, 1.6}, {0.6, 2.2}, {0.7, 2.9}, {0.8, 3.7}, {0.9, 4.6}, {1., 5.6}}

datax[2]

{{0., 0.2}, {0.1, 0.3}, {0.2, 0.5}, {0.3, 0.8}, {0.4, 1.2}, {0.5,
  1.7}, {0.6, 2.3}, {0.7, 3.}, {0.8, 3.8}, {0.9, 4.7}, {1., 5.7}}

xm = {{0.1},{0.2}};
Do[
     xm = xm + t;
     Do[dataxm[i] = Reap[Sow[{t, x[[i]]}]][[2, 1]], {i, 1, 2}]
         , {t, 0, 1, 0.1}]

dataxm[1]
{{1., {5.6}}}

 dataxm[2]
{{1., {5.7}}}