Do All Carts Need to Collide Simultaneously to Maintain Momentum Conservation?

[dandy9]

Homework Statement

Three carts of masses 4.0 kg, 10 kg, and 3.0 kg move on a frictionless horizontal track with speeds of 5.0 m/s, 3.0 m/s, and -4.0 m/s, as shown in Figure P6.34. The carts stick together after colliding. Does your answer require that all carts collide and stick together at the same time?

Homework Equations

m1v1+m2v1+m3v3 = (m1+m2+m3)v

The Attempt at a Solution

I found the final velocity of all three carts to be 2.2m/s.
The part that I'm confused about is if the carts need to collide and stick together at the same time. I tried googling it, but I kept finding different answers - some ppl saying "yes" and others saying "no". Even if I found a consistent answer, what I'm really looking for is a why?

I have a quiz tomorrow on collisions. If someone could help me out really soon I would very much appreciate it. Thank you!

 

[gneill]

Have you considered a mathematical demonstration? Derive a symbolic expression for the final velocity if all three come together at once. Then find the result of two carts collide first, then a third afterwords. Do it all symbolically and show that the end result is the same. Since the "real" cart's characteristics can be assigned to any of the variable pairs (mass and velocity), the result holds for any combination and order of collisions.