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Finding Friction's Magnitude

A block movin...

Question

A block moving with initial velocity $u = 20 m/s$ comes to rest after covering distance of $40 m$ on a rough plane. Find out coefficient of kinetic friction. (Take $g = 10 m / s^{2}$ )

0.5

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0.25

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0.75

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Data incomplete

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Solution

The correct option is A $0.5$
Given,
$u = 20 m/s$
$S = 40 m$
Using eq, $v^{2} = u^{2} + 2 a s$
$0 - (20)^{2} = 2 a \times 40$
$a = - 5 {m/s}^{2}$
Since no external force except friction is acting on the block, therefore
Frictional force = $m a$
= $5 m$
Also, friction force= $μ m g$
therefore, $μ m g$ = $5 m$
$μ g = 5$
$μ = \frac{5}{g} = 0.5$

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