A10-kg cart moving at 5 m/s collides with a 5-kg cart at rest and causes it to move 10 m/s. which principle explains the result?
a) law of differential mass
b) law of conservation of momentum
c) law of unequal forces
d) law of accelerated collision

B) law of conservation of momentum

It states that the total momentum of a system before impact is the same as the total momentum of the system after impact.

In this case total momentum before impact:

10kg*5m/s  + 5kg * 0m/s = 50 kg m/s

After Impact:

10kg*0m/s + 5kg*10m/s = 50 kg m/s

You can see the momentum before and after impact is same as 50 kg m/s  

Of course we assumed that the first cart stopped after the impact, and there are no energy losses.