Answer:
The speed of the cart decreases
Explanation:
The track is frictionless, so we can consider the cart as isolated system (no external forces acting on it): therefore, the momentum of the cart is conserved
where m is the mass and v the speed of the cart.
When it starts raining, some water falls into the cart: this means that the mass of the cart, m, increases. But we said that the momentum, p, must remain constant: in order for that to happen, this means that the speed of the cart, v, must decrease (because the relationship is an inverse relationship, so if m increases, v must decrease).