A-LevelMathematicsMechanics9709/41 · Oct/Nov 2025 · Q25 Marks

Two particles, P and Q, of masses 3 kg and 5kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 ms⁻¹ directly towards Q. After P and Q collide, P has speed 1 ms⁻¹.

(a)Find the two possible speeds of Q after the collision.[3]
(b)It is given that λ J of kinetic energy, where λ > 0, is lost during the collision. Find the value of λ.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[M1] Attempt at conservation of linear momentum; three non-zero terms – allow sign errors. M1 only if using weight rather than mass.
[A1] v = 3m s⁻¹
[A1] v = 1.8m s⁻¹ If A0 A0 SC B1 for both -3 and -1.8.
[M1] Attempt at either the total kinetic energy before or after the collision. The total KE (before and after) could be embedded in a calculation for the KE loss. M1 be awarded just on sight of 24, 19.6 or 14.4.
[A1] λ=14.4 ONLY Allow -14.4. Must have discarded λ = 0 if mentioned.

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 4 Variant 1, question 2.

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