Explicit physics instruction
For a closed one-dimensional system, Σp_before=Σp_after. Write every object’s signed momentum term before substituting numbers.
If objects stick together, they share one final velocity. If they separate, each final velocity remains a separate unknown or measured quantity.
A numerical solution should be checked against direction, magnitude, and the original system momentum.
Vocabulary: initial momentum; final momentum; perfectly inelastic; signed velocity; conservation equation.
Worked example with reasoning
A 2 kg cart at +4 m/s sticks to a stationary 2 kg cart: 8=(4)v_f, so v_f=+2 m/s.
Guided question
A 3 kg cart at +2 m/s sticks to a 1 kg cart at −2 m/s. Find the shared final velocity.
Independent work
- Solve four one-dimensional collision problems.
- For each, audit momentum before and after.
- Explain one negative velocity physically.
Misconception check
Do not drop signs when adding momentum; opposite directions are not both positive.
Formative understanding check
Why can a final velocity be negative?
Reveal response
The system’s net momentum can point in the declared negative direction.
Mentor evidence conference
Ask Archaemenes to audit the system boundary, sign convention, and conservation assumption.
Teacher guidance
Foundation: Use before/after momentum tables.
Core: Solve mixed collision directions.
Extended: Analyze sensitivity to a measured velocity uncertainty.