ARCH-P-08: 1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & Collisions

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-08: Why the 135s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~135s (Blows 90s Clock)

Write

p = mv = 12

and

E_k = \frac{1}{2}mv^2 = 18

. Divide

\frac{E_k}{p} = \frac{1}{2}v = \frac{18}{12} \implies v = 3\text{ m s}^{-1}

. Then

m = \frac{p}{v} = \frac{12}{3} = 4\text{ kg}

(~110s).

The Fast ShortcutTarget: 35s (Saves 100s)

Line 1 (Momentum-Energy Identity): Memorise

E_k = \frac{p^2}{2m} \iff m = \frac{p^2}{2E_k}

.
Line 2 (Substitute):

m = \frac{12^2}{2 \times 18} = \frac{144}{36} = 4\text{ kg}

(20s).

Where Students Lose Time: In 10 past UAT-UK questions (4.29% of Physics), candidates lose 100s by failing to assign opposite signs to approaching (+u) and rebounding (-v) velocities. Instead, apply P3 with Maths 1 skill M4.4.

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