A body starts slipping down an incline and moves half meter in half second. How long will it take to move the next half meter?
Correct option is A. $$ 0.21\,s$$
Given,
For the first half mt. $$ u =0,s=0.5m, t = 0.5\,sec.$$
$$ S = ut+1/2\,at^{2}\Rightarrow 0.5 = 0 +1/2a(0/5)^{2}\Rightarrow a = 4m/s^{2}...(2)$$
So, $$ v = u+at = 0+(0.5)4 = 2m/s $$
For the next half metre
$$u' = 2m/s, a = 4m/s^{2},s =0.5.$$
$$\Rightarrow 0.5 = 2t+(1/2)4t^{2}\Rightarrow +2t-0.5 = 0 $$
$$\Rightarrow 4t^{2}+4t-1 = 0 $$
$$\therefore = \dfrac{-4\pm \sqrt{16+16}}{2\times 4} = \dfrac{1.656}{8} = 0.207sec$$
Time taken to cover next half meter is $$0.21sec.$$