Two carts leave together

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Problem: Two carts leave together
A 2 kg cart at +5 m/s collides with a stationary 3 kg cart. They stick together.
Question: Find their common final velocity.
Givens:
- m₁ = 2 kg
- u₁ = +5 m/s
- m₂ = 3 kg
- u₂ = 0
Assumptions: One-dimensional brief impact; negligible external impulse; carts stick and share one final velocity.
Choices (LaTeX):
A. 2\ \mathrm{m\,s^{-1}}
B. 5\ \mathrm{m\,s^{-1}}
C. \sqrt{10}\ \mathrm{m\,s^{-1}}
D. 10/3\ \mathrm{m\,s^{-1}}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.