To solve this problem, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, we need to find the work done by the force to change the body's speed from 4 m/s to 6 m/s.
The initial kinetic energy of the body is given by: KE_initial = (1/2) * m * v_initial^2 = (1/2) * 2 kg * (4 m/s)^2 = 16 J
The final kinetic energy of the body is given by: KE_final = (1/2) * m * v_final^2 = (1/2) * 2 kg * (6 m/s)^2 = 36 J
The work done by the force is equal to the change in kinetic energy: Work = KE_final - KE_initial = 36 J - 16 J = 20 J
The work done by a force can be calculated as the product of the force and the distance over which it acts: Work = force * distance
We know the force magnitude is 5 N, so we can rearrange the equation to solve for the distance: distance = Work / force = 20 J / 5 N = 4 m
Therefore, the force must act over a distance of 4 meters in order to change the body's speed from 4 m/s to 6 m/s.