Question

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?

Answer 1

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.