The velocity-time graph of the figure shows the motion of a wooden block of mass 1 kg which is given an initial push at t = 0 along a horizontal table.

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The coefficient of friction between the block and the table is 0.1

The coefficient of friction between the block and the table is 0.2

If the table 'was half of its present roughness, the time taken by the block to complete the journey is 4 s

If the table was half of its present roughness, the time taken by the block to complete the journey is 8 s

answer is A, D.

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Detailed Solution

a = slope of v-t graph = -1 m/s²

$∴ Retardation = 1 m / s^{2} = \frac{μ m g}{m} = μ g$

or $μ = \frac{1}{g} = \frac{1}{10} = 0.1$

If μ is half, then retardation a is also half. So, using

$v = u - a t or 0 = u - a t$

or $t = \frac{u}{a}$ or $t \propto \frac{1}{a}$

we can see that twill be two times.

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