Step-by-step explanation:
Given that,
Mass of the cart,

Mass of the cart 2,
Final speed of cart 2,

Final speed of cart 1 is 0 as it comes to rest.
Let us assume that the initial velocity of the cart 2 is 0. So using the conservation of linear momentum as :

So, the initial velocity of the 1.0-kg cart is 0.9 m/s.