Time to travel \(100 \mathrm{m}\) is \(\mathrm{t}+\frac{1}{2} \mathrm{sec}\)

\(81=\frac{1}{2} \times \mathrm{a} \times \mathrm{t}^{2} \quad \Rightarrow \mathrm{t}=9 \sqrt{\frac{2}{\mathrm{a}}}\)

\(100=\frac{1}{2} \times \mathrm{a} \times\left(\mathrm{t}+\frac{1}{2}\right)^{2} \Rightarrow \mathrm{t}+\frac{1}{2}=10 \sqrt{\frac{2}{\mathrm{a}}}\)

\(9 \sqrt{\frac{2}{a}}+\frac{1}{2}=10 \sqrt{\frac{2}{a}}\)

\(\frac{1}{2}=\sqrt{\frac{2}{a}}\)

\(a=8 \mathrm{m} / \mathrm{s}^{2}\)