2025 CGS PRELIMS P2 Q8

2025 CGS PRELIMS P2 Q8

Secondary 4
10 marks
2025 Crescent Girls' School Prelims A Math Paper 2

A particle moves in a straight line so that \(t\) seconds after leaving a fixed point \(O\), its velocity \(v\) m/s, is given by \(v = 16(2e^{-2t} - e^{-t})\). Find

  1. the time when the particle reaches its greatest distance from \(O\),[3]
  2. the value of the greatest distance from \(O\).[3]
  3. the minimum velocity of the particle.[4]

Solution:

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Answer:(a) \(\ln2\text{ s}=0.693\text{ s}\) (b) \(4\text{ m}\) (c) \(-2\text{ m s}^{-1}\)

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