Center-of-mass velocity is the system momentum divided by total mass
The mistake
Averaging speeds without weighting by mass.
Why it feels right
Average speed feels like the middle of the listed speeds.
How to catch it
You compute v_cm = (v₁ + v₂)/2 for unequal masses.
The first principle
The center-of-mass velocity is v_cm = (Σmᵢvᵢ)/(Σmᵢ). The larger mass weights the average more strongly.
worked mini-example
A 1 kg cart moves right at 6 m/s; a 3 kg cart is at rest. What is v_cm?
Common wrong move
3 m/s.
Correct
(1·6 + 3·0)/4 = 1.5 m/s to the right.
Test the repair MOM-05 · transfer
include m/s
Make a fresh prediction before referring to the worked example.