a
(a)

Shortcut : \(S=\frac{1}{2} \frac{\alpha \beta}{\alpha+\beta} T^2\)

\(\alpha \rightarrow\) Acceleration

\(\beta \rightarrow\) Deceleration (magnitude only)

\(T \rightarrow\) Time of journey

\(S \rightarrow\) Distance travelled

Given, \(\alpha=0.2 \,ms ^{-2}\)

\(\beta=0.4 \,ms ^{-2}\)

\(T=\) half an hour \(=30 \times 60 \,s =1800 \,s\)

\(S=\frac{1}{2} \times\left(\frac{0.2 \times 0.4}{0.2+0.4}\right) \times(1800)^2\)

\(\Rightarrow S=216000 \,m\)

\(\Rightarrow S=216 \,km\)