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?

Suppose, the body is accelerating downward with an acceleration 'a'

From the free body diagram,
$R-mg\cos \theta =0\Rightarrow R=mg\cos \theta and-ma+mg\sin \theta -\mu R=0\Rightarrow a=mg(sin\theta -\mu \cos \theta )/m=g(\sin \theta -\mu \cos \theta )$
For the first halfmeter,
$u=0,S=5m,So,v=u+at=0+\left(0.5\right)4=2m/secFromS=ut+\frac{1}{2}a{t}^{2}0.5=0+\frac{1}{2}a(0.5{)}^2\Rightarrow a=4m/s^2$
For the next half metre,
$u=2m/sec,a=4m/s^2,S=0.5\Rightarrow 0.5=2t+\left(\frac{1}{2}\right)4t^2\to 2l^2+t-0.5=0\Rightarrow 4t^2+4t-1=0\Rightarrow t=\frac{-4\pm \sqrt{16}+16}{2\times 4}=\frac{1.656}{8}\simeq 0.2027$
Time taken to cover next half meter is 0.21 sec.