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A particle is performing rectilinear motion on \( x \) axis, such that its \( x \)-coordinate varies with time as \( x=\frac{t^{3}}{3}-2 t^{2}+3 t+5(\mathrm{~m}) \) where \( t \) is in second. In column I, time instant is given and column II describes the motion of particle at particular instant. Match the proper entry from column II to column I.
\begin{tabular}{|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column I } & \multicolumn{1}{c|}{ Column II } \\
\hline i. \( \quad t=\frac{1}{2} \mathrm{sec} \) & a. Particle is moving in positive \( x \)-direction and speeding up. \\
\hline ii. \( t=\frac{3}{2} \mathrm{sec} \) & b. Particle is moving in negative \( x \)-direction and slowing down. \\
\hline iii. \( t=\frac{5}{2} \mathrm{sec} \) & c. Particle is moving in negative \( x \)-direction and speeding up. \\
\hline iv. \( t=4 \mathrm{sec} \) & d. \( \quad \) Particle is moving in positive \( x \)-direction and slowing down \\
\hline
\end{tabular}
(1) i \( \rightarrow \) d; ii \( \rightarrow \) c; iii \( \rightarrow \) b; iv \( \rightarrow \) a
(2) i \( \rightarrow \) a; ii \( \rightarrow \) c; iii \( \rightarrow \) b; iv \( \rightarrow \) d
(3) i \( \rightarrow \) a; ii \( \rightarrow \) b; iii \( \rightarrow \) c; iv \( \rightarrow \) d
(4) i \( \rightarrow \) d; ii \( \rightarrow \) b; iii \( \rightarrow \) c; iv \( \rightarrow \) a
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