Final answer:
The friction force acting on the box cannot be precisely determined with the given information as the applied force is unknown. We can only calculate the net force based on the mass and acceleration. Once the applied force is known, we could subtract the net force from it to find the friction force.
Step-by-step explanation:
To calculate the friction force acting on a 12.0 kg box that accelerates to a final velocity of 5.0 m/s in 12 seconds from rest, we can use Newton's second law and the equation for kinetic friction. First, we calculate the acceleration (a) of the box: a = (v - u) / t, where v is the final velocity, u is the initial velocity (0 m/s, since it starts from rest), and t is the time. So, a = (5.0 m/s - 0 m/s) / 12 s = 0.4167 m/s².
Then, we calculate the net force (Fnet) applied to the box using Newton's second law, Fnet = m*a, where m is the mass of the box. Therefore, Fnet = 12.0 kg * 0.4167 m/s² = 5.0 N. Since the box is accelerating, we know there must be an applied force Fapp that is greater than the friction force Ffric.
Finally, to find the friction force, we need to consider that the net force is the difference between the applied force and the friction force: Fnet = Fapp - Ffric, and since the acceleration is not zero, there must be an applied force causing the motion. Without knowing the applied force, we cannot determine the exact friction force. If the applied force were known, we could rearrange the equation to solve for friction force: Ffric = Fapp - Fnet.