a
(a) If \({t_1}\) and \(2{t_2}\) are the time taken by particle to cover first and second half distance respectively.

\({t_1} = \frac{{x/2}}{3} = \frac{x}{6}\)…(i)

\({x_1} = 4.5\;{t_2}\) and \({x_2} = 7.5\;{t_2}\)

So, \({x_1} + {x_2} = \frac{x}{2} \Rightarrow 4.5{t_2} + 7.5{t_2} = \frac{x}{2}\)

\({t_2} = \frac{x}{{24}}\)…(ii)

Total time \(t = {t_1} + 2{t_2} = \frac{x}{6} + \frac{x}{{12}} = \frac{x}{4}\)

So, average speed \( = 4\;m/sec\).