Newton's Third Law predicts that during a collision between two carts, when the sum of the forces acting on the system are zero:

The two carts will experience an impulse of the same magnitude, but of opposite directions.

Explanation:

Newton's third law proves that though action and reaction are the same, but they are opposite to each other.

i.e = -

where: and have equal value.

Impulse = F x t

where F is the force on the object and t is the time of impact.

In the given question, since the collision takes place in a given time.

Then;

x = - x

⇒ = -

Thus, since the sum of the forces acting on the system are zero, then the two carts experience an impulse of the same magnitude but opposite in directions.