Final answer:
The acceleration of the box is 1.305 m/s^2.
Step-by-step explanation:
To find the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
First, let's calculate the force of kinetic friction using the coefficient of kinetic friction. The formula to calculate the force of kinetic friction is f k = μkN, where f k is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.
The normal force is equal to the weight of the box, which is the mass of the box multiplied by the acceleration due to gravity (N = mg). Substituting the given values, we get N = (10.0 kg)(9.8 m/s^2) = 98 N.
Now we can calculate the force of kinetic friction as f k = (0.275)(98 N) = 26.95 N.
The net force acting on the box is given by the applied force minus the force of kinetic friction (Fnet = F - f k).
Substituting the given values, we get Fnet = 40.0 N - 26.95 N = 13.05 N.
Finally, we can calculate the acceleration of the box using Newton's second law. The formula is a = Fnet/m, where a is the acceleration, Fnet is the net force, and m is the mass of the box.
Substituting the given values, we get a = 13.05 N / 10.0 kg = 1.305 m/s^2.