Final answer:
The magnitude of the acceleration of the box after it starts moving is 4.91 m/s^2, calculated by using the force of kinetic friction and applying Newton's second law.
Step-by-step explanation:
To find the magnitude of the acceleration of the box after it starts moving, we first need to calculate the force of kinetic friction, which is given by f-k = μkN, where μk is the coefficient of kinetic friction and N is the normal force. For a box resting on a level surface, the normal force is equal to the gravitational force on the box, thus N = mg. With a mass (m) of 44 kg and g as 9.81 m/s2, we get N = 44 kg × 9.81 m/s^2 = 431.64 N. Using the coefficient of kinetic friction (μk) of 0.5, the kinetic frictional force would be f-k = 0.5 × 431.64 N = 215.82 N.
Once the box starts moving, the only horizontal force acting against it is the force of kinetic friction. To determine the acceleration, we use Newton's second law, F = ma, where F is the net force acting on the box, m is the mass, and a is the acceleration. Since the only horizontal force once the box is moving is the kinetic friction, F equals -f-k. Therefore, a = -f-k / m = -215.82 N / 44 kg ≈ -4.91 m/s^2. The negative sign indicates that the acceleration (slowing down due to friction) is in the direction opposite to the motion.
Thus, the magnitude of the acceleration of the box after it starts moving is 4.91 m/s^2.