Final answer:
The system of interest for calculating the child's acceleration includes both the child and the wagon. The acceleration can be calculated using Newton's second law of motion by considering the net force and the mass of the system. In this case, the expected acceleration is -0.54 m/s² in the opposite direction of motion.
Step-by-step explanation:
The system of interest for calculating the acceleration of the child in the wagon is the child and the wagon together. This is because both the child and the wagon are part of the same system and can be considered as one object.
To calculate the acceleration, we need to use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the net force is the sum of the forces exerted by the two children pushing in opposite directions, minus the force of friction.
Using the given values, the net force is 75 N - 90 N - 12 N = -27 N (opposite direction of motion). The total mass of the child and the wagon is 50 kg. Applying Newton's second law, we have:
Acceleration = Net force / Mass = (-27 N) / (50 kg) = -0.54 m/s²
So, the expected acceleration of the child in the wagon is -0.54 m/s² in the opposite direction of motion.