Explanation

(c) $\because S_{1} = ut + \frac{1}{2}at^{2}\ \ \ \ \ldots(i)$
and velocity after first $t\ sec$
$v = u + at$
Now, $S_{2} = vt + \frac{1}{2}at^{2}$
$= (u + at)t + \frac{1}{2}at^{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
Equation $(ii) - (i) \Rightarrow S_{2} - S_{1} = {at}^{2}$
$\Rightarrow a = \frac{S_{2} - S_{1}}{t^{2}} = \frac{65 - 40}{(5)^{2}} = 1m/s^{2}$
From equation (i), we get,
$S_{1} = ut + \frac{1}{2}at^{2} \Rightarrow 40 = 5u + \frac{1}{2} \times 1 \times 25$
$\Rightarrow 5u = 27.5\ \therefore u = 5.5\ m/s$