A body begins slipping down an incline, travelling half a meter in...

Since the body starts from rest, the distance covered is given by $s = \dfrac{1}{2}at^2$, which implies $t \propto \sqrt{s}$.

Let $t_1$ be the time taken to cover the first distance $s_1 = 0.5$ m, and $t_2$ be the total time taken to cover the total distance $s_2 = 0.5 + 0.5 = 1$ m.

$\dfrac{t_2}{t_1} = \sqrt{\dfrac{s_2}{s_1}}$

$\dfrac{t_2}{0.5} = \sqrt{\dfrac{1}{0.5}} = \sqrt{2}$

$t_2 = 0.5\sqrt{2} \approx 0.5 \times 1.414 = 0.707$ s

The time required to move the subsequent half meter is:

$\Delta t = t_2 - t_1 = 0.707 - 0.5 = 0.207$ s

Rounding off to two decimal places, we get $0.21$ s.