2025 BDS PRELIMS P2 Q5

2025 BDS PRELIMS P2 Q5

Secondary 4
10 marks
2025 Bedok South Secondary School Prelims A Math Paper 2

A particle moves in a straight line so that, at time \(t\) seconds after passing a fixed point \(O\), its velocity is \(v\) m/s, where \(v = 4 + 8\cos 2t\). Find

  1. the velocity of the particle at the instant it passes \(O\),[1]
  2. the least value of the particle’s acceleration,[1]
  3. the values of \(t\), in terms of \(\pi\), when the particle is at rest for \(0 \leq t \leq 3\),[4]
  4. the distance travelled in the first 2 seconds.[4]

Solution:

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Answer:(a) \(12\text{ m/s}\). (b) \(-16\text{ m/s}^2\). (c) \(\pi/3,2\pi/3\) seconds. (d) \(8\pi/3+4\sqrt3-8-4\sin4\text{ m}\approx10.3\text{ m}\).

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