SPM 2020 Add Maths Paper 2, Question 12Kinematics of Linear Motion

Solved on video in English and Bahasa Melayu · Form 5, Kinematics of Linear Motion · 6:10 video

The question

(a)

(Solution by graph sketching is NOT accepted.) Diagram 6 shows particle P and particle Q moving along a straight line through a fixed point O, with A----21 m----O----33 m----B (P starts at A, Q starts at B). Particle P starts moving from A and particle Q starts moving from B simultaneously. After t seconds, the velocity (v ms⁻¹ of P is vP = 2t - 4 and of Q is vQ = 8 - 2t. (a) Determine which particle passes through the fixed point O first. Hence, state the time, in seconds.

(b)

(b) The two particles meet after k seconds. Find the value of k.

(c)

(c) Find the furthest distance, in m, between particle P and particle Q during the motion.

SPM 2020 Add Maths Paper 2, Question 12: the question as drawn in Eduly's video6:10

Part (a)

Step 1

Displacement (measured from each particle's start, taking A as origin for both): integrate velocity.

Why this step

Velocity only tells us how fast position changes. To get position we integrate, and skipping this is where weaker candidates lose marks.

5 more steps, each with the reason for it, in the full solution

Final answer

P passes O first, at t = 7 s

Where students lose marks

Watch out: measure both positions from A, so Q's constant is 54, not 0. Then clearly state the time, t = 7 s.

Part (b)

5 more steps, each with the reason for it, in the full solution

Final answer

k = 9

Where students lose marks

Watch out: 'meet' means equal positions (sP = sQ), not equal velocities. Setting vP = vQ finds a different moment.

Part (c)

5 more steps, each with the reason for it, in the full solution

Final answer

72 m

Where students lose marks

Watch out: use one gap g(t) = sQ − sP at a single time. Adding each particle's turning-point distance (74 m) mixes different times.

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