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Calculating acceleration from displacement measurements

I have a table of measurements s(t):

t[s], s[m]

  1. 0, 0
  2. 12.48, 26.4
  3. 18.06, 52.8
  4. 22.32, 79.2

I have calculated all values for $a$ using $$ a=\frac{2s}{t^2} $$ and simply sticking the values into the formula for each measurement.

I have read here that one should instead use the formula $$ s=ut\ +\ \frac{1}{2}at^2, $$ which can be used for the first measurement since $u=0$ (which is then effectively the same formula I used). My problem is that I don't know how to calculate values for $u$ for each measurement and thus calculate $a$ correctly. Is there perhaps another way? Am I doing something wrong?