Blaw 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:
10kg5m/s + 5kg 0m/s = 50 kg m/s
After Impact:
10kg0m/s + 5kg10m/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.
