What uhhhhhhhhhhhhhhhhhhhhh
The cart is moving by simple harmonic motion, and its position at time t is described by

where
A is the amplitude of the oscillation

is the angular frequency
The amplitude of the oscillation corresponds to the maximum displacement of the spring, which corresponds to the initial position where the spring was released:
A=0.250 m
The period of the motion is T=5.67 s, and the angular frequency is related to the period by

Therefore now we can calculate the position of the system at the time t=29.6 s:
There are different forces acting on an object like nuclear force , gravitational force...plus external forces like friction and other..
net sum of all these is resultnat
since child is moving along with the wagon and we need to find the acceleration of child inside that wagon then in this case the system of interest must be child + wagon
System of interest will be the system that is used to find the force or acceleration using Newton's law
Here we have to assume that system on which if we will calculate the forces then the net value of force on that system will help to calculate the unknown quantities
So here our system will be boy + wagon