Question

There is no friction anywhere. The cart system is let go with everything initially at rest. Find the acceleration for each of the three masses relative to ground. (they are all different)

Answer 1

How should I approach this? I have no idea where to start

Answer 2

you can start drawing free body diagrams for each block, to do that you will need to identify the forces acting on each of them first. for example for block 3:

only the tension force \(T\) and the wight \(W_3\) are acting on this block.
try to do the same for the other blocks, and then write down the force sum for each of them.
If you get the diagrams done right you can get the equations directly from them.