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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-VM-0032 marksL1 FoundationCalculatorPosition
A particle starts at the point with position vector (2i+j)(2\mathbf i+\mathbf j) m and moves with constant velocity (3i−2j) m s−1(3\mathbf i-2\mathbf j)\ \text{m s}^{-1}. Its position after 44 s is (pi+qj)(p\mathbf i+q\mathbf j) m. Find pp and qq.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0012 marksL1 FoundationNon-calculatorPosition
A particle starts at (4i−j)(4\mathbf i-\mathbf j) m and moves with constant velocity (2i+3j)(2\mathbf i+3\mathbf j) m s⁻¹. Its position after 55 s is (pi+qj)(p\mathbf i+q\mathbf j) m. Find pp and qq.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0021 markL1 FoundationNon-calculatorVelocity & acceleration
A particle has velocity (5i−12j)(5\mathbf i-12\mathbf j) m s⁻¹. Find its speed.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0061 markL1 FoundationNon-calculatorVelocity & acceleration
A particle moves from (i+j)(\mathbf i+\mathbf j) m to (9i+7j)(9\mathbf i+7\mathbf j) m in 22 s at constant velocity. Find its speed.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM-Q011 markL1 FoundationCalculatorVelocity & acceleration
A velocity is (6i−8j) m s−1(6\mathbf i-8\mathbf j)\ \text{m s}^{-1}. The speed is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-VM-Q021 markL1 FoundationCalculatorPosition
A particle is due north of the origin when its position vector
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-VM-0043 marksL2 StandardCalculatorVelocity & acceleration
A particle's velocity changes from (2i+3j)(2\mathbf i+3\mathbf j) to (8i−5j) m s−1(8\mathbf i-5\mathbf j)\ \text{m s}^{-1} in 22 s, with constant acceleration. Find the magnitude of the acceleration.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM-0062 marksL2 StandardCalculatorPosition
A ship's position at time tt hours is r=[(−10+2t)i+(5+3t)j]\mathbf r=[(-10+2t)\mathbf i+(5+3t)\mathbf j] km. Find when it is due north of the origin.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0032 marksL2 StandardNon-calculatorPosition
A boat's position at time tt hours is r=[(6+3t)i+(4t−8)j]\mathbf r=[(6+3t)\mathbf i+(4t-8)\mathbf j] km. Find the time when it is due east of the origin.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0043 marksL2 StandardNon-calculatorVelocity & acceleration
A particle has initial velocity (2i+j)(2\mathbf i+\mathbf j) m s⁻¹ and constant acceleration (i−2j)(\mathbf i-2\mathbf j) m s⁻². Find its speed after 33 s.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM2-0054 marksL3 ExamNon-calculatorPosition
Ship AA is at rA=[(2+t)i+(3+2t)j]\mathbf r_A=[(2+t)\mathbf i+(3+2t)\mathbf j] km and ship BB at rB=[(8−t)i+(−3+4t)j]\mathbf r_B=[(8-t)\mathbf i+(-3+4t)\mathbf j] km, at time tt hours. Find the time at which the ships would collide.

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Salam Academy Original Practice · Proposed mark scheme
SA-VM-0086 marksL4 ChallengingCalculatorVelocity & acceleration
A particle PP moves with constant velocity. At t=0t=0 it is at (i+2j)(\mathbf i+2\mathbf j) m, and at t=3t=3 s it is at (7i−4j)(7\mathbf i-4\mathbf j) m. Find (i) its speed, to 3 significant figures, and (ii) the time when it is due east of the origin.

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Salam Academy Original Practice · Proposed mark scheme