Introduction:
In order to understand the force required to keep a body moving with a constant velocity, we need to consider the concept of Newton's second law of motion and the forces acting on the body.

Newton's Second Law of Motion:
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be represented as:

F = ma

Where F is the net force acting on the object, m is the mass of the object, and a is the acceleration produced.

Forces Acting on the Body:
In this scenario, the body is initially moving with a velocity of 4m/s and comes to rest after 2 seconds. We can assume that the body is experiencing a retarding force, which is causing it to decelerate and eventually come to rest.

The force acting on the body can be calculated using the equation:

F = ma

Since the body comes to rest, the final velocity (vf) will be zero. The initial velocity (vi) is given as 4m/s, and the time taken (t) is given as 2 seconds.

Using the equation of motion:

vf = vi + at

Substituting the given values, we can calculate the acceleration (a):

0 = 4 + a * 2

a * 2 = -4

a = -2 m/s^2 (negative sign indicates deceleration)

Force Required to Maintain Constant Velocity:
In order to keep the body moving with a constant velocity of 4m/s, an external force must be applied to counteract the retarding force. This external force should be equal in magnitude and opposite in direction to the retarding force.

Since the body is moving on a horizontal surface, the only force acting on it is the force of friction. The force of friction can be calculated using the equation:

Ffriction = μ * N

Where μ is the coefficient of friction and N is the normal force.

In this scenario, since the body is on a horizontal surface, the normal force is equal to the weight of the body, which can be calculated as:

N = mg

Where m is the mass of the body and g is the acceleration due to gravity.

The force required to maintain constant velocity can be calculated as:

Frequired = Ffriction = μ * N = μ * mg

Substituting the given values, we can calculate the force required:

Frequired = μ * 2 * 9.8

Conclusion:
The force required to keep the body moving on the same surface with a velocity of 4m/s is equal to the force of friction, which can be calculated using the equation Frequired = μ * mg. The frictional force depends on the coefficient of friction and the weight of the body.

V=u+at
0=4+a×2
a=-2m/s²
F=ma
F=2×2
F=4N