Center-of-mass velocity is the system momentum divided by total mass

01
The tempting model
Averaging speeds without weighting by mass.
02
Why it feels right
Average speed feels like the middle of the listed speeds.
03
Where it breaks · how to catch it
You compute v_cm = (v₁ + v₂)/2 for unequal masses.
04
The correct model
The center-of-mass velocity is v_cm = (Σmᵢvᵢ)/(Σmᵢ). The larger mass weights the average more strongly.
05
Repair · see it, then test it
worked example A 1 kg cart moves right at 6 m/s; a 3 kg cart is at rest. What is v_cm?
Tempting move
3 m/s.
Correct move
(1·6 + 3·0)/4 = 1.5 m/s to the right.
Test the repair MOM-05 · transfer

A 2.0 kg cart moves right at 3.0 m/s while a 1.0 kg cart moves left at 3.0 m/s. What is v_cm, taking right as positive?
include m/s

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R25Center-of-mass velocityadds: The center-of-mass velocity is total momentum over total mass.