Which situation will produce the greatest change of momentum for a 1.0-kilogram cart?

Momentum is the product of mass of an object or a body and the velocity. According to second newtons' law of motion the resultant force is directly proportional to the rate of change in momentum.

Therefore, F = (mv-mu) / t where m is the mass, v - final velocity and u - initial velocity.

Change in momentum is mv-mu, which can be given by Ft (impulse) from the law.

Therefore in this case, the change in momentum will be higher when a net force of 5 N is applied for 2 seconds. (change in momentum = (5*2) = 10)