Modified Atwood machine that *slows down*

The problem above is from 5 Steps to a 5: AP Physics 1, the "Elite Student Edition."  This situation provides an opportunity to find out how well students are doing with understanding the meaning of acceleration.

Ask: immediately after the carts are pushed or released, in which experiment is the magnitude of the carts' acceleration greater?  And, are the directions of the top cart's acceleration the same, or different, in the two experiments?

The correct answer refers to free body diagrams of both carts in each experiment.  The hanging block experiences forces from the rope and the earth; the only unbalanced force on the top block is that of the rope.*

*Yes, the top block also experiences balanced forces from earth and the surface.  Those aren't relevant to the acceleration, because they are balanced. 

Those free body diagrams are the same in both experiments!  By Newton's second law, the same unbalanced force acting on the same mass causes the same amount of acceleration.  And similarly, because the unbalanced force is in the same direction in each experiment, the accelerations have the same direction.  Done.

But what about the initial push?  All forces other than gravity** require contact.  While I was pushing the cart, the cart experienced a force from my hand.  After that - and the question explicitly is asking about AFTER the cart has been pushed - my hand isn't touching the cart, and so cannot apply a force.

** in mechanics, anyway

Okay, but isn't the cart on the surface moving to the right in Experiment B?  So its acceleration is in a different direction than in Experiment A, when the cart moves to the left.

Um, no - here is precisely the misconception this question is designed to test!  Motion is emphatically NOT the same thing as acceleration.  

When an object speeds up, its acceleration is the same as the direction of motion.  When an object slows down, its acceleration is opposite the direction of motion.  

In Experiment A, the cart is moving left and speeding up, giving it a leftward acceleration.  In Experiment B, the cart is moving right and slowing down.  Thus, its acceleration is opposite the direction of motion... so the acceleration is also leftward.