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UAT-UK SPEC: P3MODULE: PHYSICSTOPIC ID: ARCH-P-08

1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions

Master 1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions on the ESAT Physics paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 35s, saving +100s per question.

Standard Classroom Time
135s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
35s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+100s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Momentum-Energy Identity): Memorise Ek=p22m  ⟺  m=p22EkE_k = \frac{p^2}{2m} \iff m = \frac{p^2}{2E_k}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Substitute): m=1222×18=14436=4 kgm = \frac{12^2}{2 \times 18} = \frac{144}{36} = 4\text{ kg} (20s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1sign_or_direction_flip

Calculating rebound momentum change as m(v - u) instead of m(v - (-u)) = m(v + u)

Failing to assign opposite signs to approaching (+u) and rebounding (-v) velocities.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2subsystem_isolation_trap

Dividing total momentum by m₁ instead of coalesced mass (m₁ + m₂) after an inelastic collision

Forgetting that stuck-together trolleys move with combined mass m₁ + m₂.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3sign_or_direction_flip

Adding instead of subtracting initial momenta m₁*u₁ + m₂*u₂ when trolleys move towards each other

Treating momentum as a scalar rather than a signed 1D vector.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: 1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions

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Full Lesson All 15 Questions (ARCH-P-08)
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ARCH-P-08: 1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions (Sample)Physics
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SUB-90 ZONE (<40S)
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Question 1 of 1ARCH-P-08 (6-Card Lesson)Format: Standard 5-Option
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