Carts gaining and losing mass: What happens to velocity?

1. The problem statement, all variables and given/known data
There are 2 versions of the problem that I’ve heard:

A bucket on wheels is moving at a constant velocity on a frictionless surface. It’s raining out so the bucket is gaining mass. Will it slow down, speed up, or remain at that velocity as it gains mass?

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:
A. Constant, forwards
B. Constant, backwards
C. Variable, forwards
D. Variable, backwards
E. Zero

3. The attempt at a solution

The answer to the first one is that it will slow down because it gains mass. The answer to the second one, however, is E, that it does not decelerate and will keep its initial velocity. So what gives? What’s the difference between these answers?

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