Final answer:
The force of friction encountered by the sliding carton on the rough surface is zero. In order to determine the force of friction acting on a sliding carton, Newton's second law of motion is employed.
Step-by-step explanation:
In order to determine the force of friction acting on a sliding carton, Newton's second law of motion is employed, expressing force as the product of mass and acceleration.
In this scenario, the carton comes to a stop within 3 seconds, allowing the calculation of acceleration using the formula a = 2*(displacement)/(time^2).
Since the carton's displacement is 0 (as it stops), the acceleration is also 0.
Substituting the carton's mass into the force formula, force = mass * acceleration, results in force = mass * 0, leading to a force of friction encountered by the carton equal to zero.
This conclusion arises from the absence of acceleration due to the carton's coming to a halt, indicating a lack of net external forces acting on it during the deceleration process.