All "moving" makes sense only relative to a frame. As there is no absolute frame, for all discussions one need to choose one. It seems that any other frame than the one fixed to the enter portal is arbitrary. How do you distinguish a moving portal from everything else moving around it? Thus the only canonical answer seems to be you preserve the relative speed versus the enter portal as the speed relative to the exit portal. (B)

Both portals stationary: object velocity unchanged.

Both portals moving at the same speed: object velocity unchanged.

Entry portal moving: object pushed out at the same speed it entered.

Exit portal moving faster than object entered: object explodes.

My take:

The cube's mass is x (eg one gram) and its velocity is zero, therefore its momentum (m*v) is zero. Objects in motion tend to stay in motion, while objects at rest (e.g. momentum of zero), tend to stay at rest.

The thing which is moving, is the portal. At best, the event horizon of it reaches the leading-end then the trailing-end of the cube at the speed the portal is moving over the depth of the cube. If the portal moves faster, that distance is covered faster, and the full cube is entirely on the other end of the other portal faster [than a slower moving portal].

Since going through the portal is a frictionless and forceless action, the speed at which the portal fully envelops the cube would neither add nor remove momentum upon it. And if the cube did have its own momentum it would be maintained, but since it does not, the cube would not move until another force, like gravity, acted upon it.

So, A.

A

In this example, the object wasn’t moving. It has no momentum to continue moving. Instead, the world around it moved. So A

A 🔥

Most likely option is it flops out but only if the angle is sufficient for the cube to overcome its centre of gravity and topple. And do so before the orange portal rises again. Also depends if the downward orange portal directly touches the base or not, since there might be a bit of a "lip" to overcome too.

It went through the portal at speed, so it should exit the portal at speed. That’s my take.

It depends. It looks like the orange portal is being moved by a hydraulic cylinder (aka laminar flow), which means the relative positions and velocities of things moving through the orange portal are conserved, and A is correct.

If instead that's (yuck) an air fired cylinder... Then it's going to be B.

If the movement is handled by a threaded rod, then the box will emerge from the blue portal spinning, and (perhaps contrary to expectations) if the orange portal is moving because of gravity, then the bouyant force of the box progressing through the portal will stop it from falling further, and the box will end up just less than halfway (because of the angle) through the blue portal.

The answer is definitely B (see other comments), but I think the more interesting question is, how does it affect the portals themselves and the surfaces they're attached to?

When the portals are attached to a solid unmovable wall (as in the games), we can pretty much ignore the forces acting upon the wall as they will just be automatically cancelled out by the normal force. But the same does not apply for portals attached to detached panels. Let's say that instead of a piston pushing down, the portal is attached a free-falling panel with the portal facing down.

We are inclined to assume that as the portal falls onto the cube, it feels no force, as if it fell through air or through a vacuum. But is that really the case? Maybe instead, the falling portal experiences resistance from the cube? Or even, actually, an accelerating force?

Let's assume conservation of momentum at each end of the portal. That is, in the general case: if the portal (which we assume has no mass) is attached to an object with mass M and velocity V, and "swallows" a cube or other object with mass m and velocity v, and at the end of this interaction the portal-surface object with mass M has velocity V', then we expect:

M × V' = (M × V) + (m × v)

Mass is not conserved because the cube was transferred to the other portal.

Solve for V':

V' = V + (m/M) v

This is a strange result. The cube's momentum is imparted into the portal, but the result would be different depending on our reference frame. From a reference frame tracking the cube pre-interaction, v = 0 (by definition) and so V' = V, the portal-surface object has no change in velocity. But in any other reference frame, it does.

Physics can't be affected by reference frame (thanks, relativity) so this analysis must be wrong.

... I'll keep thinking on this.

a. while the portal travels down it collects air, increasing air pressure on the other side, meaning once it reaches the cube, the increased air pressure has mad the air solid so the cube cant fly through it.

The "ragebait answers only" in the OP is the only thing stopping me from actually raging at everyone saying A. I am giving them all the benefit of the doubt, they're deliberately saying the wrong answer.

Everyone saying B missed the assignment and answered accurately.

A. Object momentum relative to the world is retained thru portals regardless of the speed of the portal surface or the portal itself. The portal is only transmitting matter from A to B, it does not impart energy of any kind.

Real world B. In-game, A

I reject your reality and substitute my own.

The correct answer is C: the cube plops out and the object to which the blue portal is affixed flies off in the southwest direction.

A if it's a cube. B if it's beans.

Edit: Obligatory bean tax

B.

As the cube enters the portal, it will take on energy from the piston, slowing the piston down in the process, and that energy will propel it out. If it enters the portal fast, it has to exit the portal fast.