Arailway wagon of mass 20t is moving along a level track at 10km/h when it collides and couples together with a second wagon of mass 25t moving in the
same direction at 5km/h. if the two wagons couple together after the impact, what would be their common velocity?

Using conservation of momentum, you have the total initial momentum in the system is wqual to the total final momentum in the system.

mv + mv = mv

plug in all the values

(20t)(10) + (25t)(5) = (45t)Vfinal

distribute everything

200t + 125t = 45t Vf

simplify

325t = 45t Vf

divide both sides by 45t

7.22 = Vf

So their final common velocity is 7.22km/h in the same direction as they were travelling before

As newton's first law states a object in motion stays in motion