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A block of mass $2.0 kg$ is given an initial velocity of $3 m / s$ on a horizontal table where the coefficient of friction is $0.2 .$ The distance covered by the block before it stops is ____.

Take $g = 10 m / s^{2}$ .

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Detailed Solution

The distance covered by the block before it stops is

2.25 m

.
Work Energy Theorem,
Work done by external force + Work done by conservative and non-conservative forces
= Change in Kinetic Energy
Here, an external force is a frictional force, which is =

weight \times coeff . Of friction

For the block, in the system under consideration, the statement of the work-energy theorem can be written as

W_{mg} = W_{N} = K_{fk} = K_{2} - K_{1}

\Rightarrow

0 + 0 + {μ_{k} mg \times s}_{}

0 - \frac{1}{2} m {v^{2}}_{0}

⇒

s = \frac{{v_{0}}^{2}}{2 μ_{k} g}

\frac{(3)^{2}}{2 \times 0.2 \times 10}

=2.25m

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