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Further Mathematics Paper 2, May/June. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength



Question 8

The position vector of a body, with respect to the origin, is given by
r = 4t i + (12 – 3t) j at any time t seconds.

(a)  Find the velocity of the body.
(b) Calculate the magnitude of the displacement between t = 0 and  t = 5.

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Observation

In part (a), candidates were expected to differentiate the position vector r with respect to t to obtain the velocity (v) i.e. dr/dt = v = 4i – 3j.

The magnitude of the displacement required in part (b) was determined by substituting the values t = 0 and t = 5 in the equation r = 4ti + (12-3t)j and obtaining their difference i.e.  when t = 0, r = 12j when t = 5, r = 20i -3j.  Hence displacement = 20i – 3j -12j = 20i – 15j.  Required magnitude = √20² + (15)²   = √625 = 25 units.

Majority of the candidates were reported to have performed well in this question.  They were able to handle the differentiation quite well and they displayed a good knowledge of the magnitude of a vector.

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