**Analysis:**

To solve this problem, we will use the equations of motion and the concept of work and energy.

**Equations of Motion:**

The equations of motion for an object moving along a straight line are:

1. v = u + at
2. s = ut + (1/2)at²
3. v² = u² + 2as

where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time taken
- s is the displacement or distance traveled

**Force of Friction:**

The force of friction acting on the block is given by the equation:

f = μN

where:
- f is the force of friction
- μ is the coefficient of kinetic friction
- N is the normal force

In this case, the normal force is equal to the weight of the block, since it is on a horizontal surface. The weight of the block is given by:

N = mg

where:
- m is the mass of the block
- g is the acceleration due to gravity

**Applying Newton's Second Law:**

The net force acting on the block is given by:

F_net = ma

Since the block is coming to rest, the net force is equal to the force of friction:

F_net = f

Therefore,

ma = μmg

**Applying Work-Energy Principle:**

The work done by the force of friction is given by:

W = f * s

The work done is equal to the change in kinetic energy:

W = (1/2)mv² - (1/2)mu²

**Solving for Distance Traveled:**

Substituting the equations for force of friction and work done, we have:

μmg * s = (1/2)mv² - (1/2)mu²

Rearranging the equation, we get:

s = (v² - u²) / (2μg)

Substituting the given values:
- v = 0 (since the block comes to rest)
- u = 10 m/s
- μ = 0.1
- g = 9.8 m/s²

s = (0² - 10²) / (2 * 0.1 * 9.8)

s = -100 / (2 * 0.1 * 9.8)

s = -100 / 1.96

s ≈ -51.02 m

Since distance cannot be negative, the block will travel approximately 51.02 meters before coming to rest.

Due to friction , the body will decelerate.Let the deceleration be a.R-mg=0.R=mg----------------(1)
Now, ma-μR=0.ma=μmg.a= μg=0.1 x10=1m/s2.Initial velocity =u=10m/s2.Final velcoity =v=0 m/s.a=-1 m/s2.So from second equation of motion:S=v²-u²/2a.=0- 10²/2x-1.=100/2.=50m.
So, it will travel 50m before coming to rest....