A block is shot with an initial velocity of $5 m / s$ on a rough horizontal plane. Find the distance covered by the block till it comes to rest. Given coefficient of friction between the surfaces of contact is $0.1 and g = 10 m / s^{2}$ .

5 m

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10 m

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12.5 m

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25 m

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Solution

The correct option is C $12.5 m$
The given situation is shown below

The block will be under the impact of frictional force after getting shot. This will cause retardation. Hence, the acceleration of the block is given by
$F = m a = - f$
$\Rightarrow f = μ N$
$\Rightarrow - μ N = m a$
$\Rightarrow - μ m g = m a$
$a = - μ g = 0.1 \times 10 = - 1 m / s^{2}$

Given, $u = 5 m / s, a = - 1 m / s^{2}, and v = 0$
From the equation of motion we have
$\Rightarrow v^{2} - u^{2} = 2 a s \Rightarrow 0^{2} - 5^{2} = - 2 (1) (s)$
$\Rightarrow s = 12.5 m$

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