Final answer:
To determine the final speed of the box after sliding across the rough section of flooring, we can use energy considerations. The work done by the kinetic frictional force is equal to the change in kinetic energy. The final velocity of the box can be calculated using the equation for work and the given coefficients and distances.
Step-by-step explanation:
To determine the final speed of the box after sliding across the rough section of flooring, we can use energy considerations. Since the box is sliding on a horizontal frictionless floor before encountering the rough section, the only force acting on it is the kinetic friction. The work done by the kinetic frictional force can be calculated using the equation work = force of friction × distance.
Given that the coefficient of kinetic friction is 0.100 and the distance is 4.50 m, we can calculate the force of friction using the equation force of friction = coefficient of kinetic friction × normal force. Since the floor is horizontal and frictionless, the normal force is equal to the weight of the box.
The work done by the kinetic frictional force is equal to the change in kinetic energy.
Therefore, we can use the equation work = change in kinetic energy = (1/2) × mass × (final velocity)² - (1/2) × mass × (initial velocity)² to find the final velocity of the box after sliding across the rough section.