2025 BVSS PRELIMS P2 Q9

2025 BVSS PRELIMS P2 Q9

Secondary 4
11 marks
2025 Bedok View Secondary School Prelims A Math Paper 2

A particle moves in a straight line so that its acceleration, \(a\ \text{m/s}^2\), is given by \(a=-2\cos \frac{1}{2}t\), where \(t\) is the time in seconds after leaving a fixed point \(O\).

  1. Sketch the acceleration-time graph of the particle for \(0\leq t\leq 2\pi\).[2]
  2. The initial velocity of the particle is \(3\ \text{m/s}\). Find the earliest time when the particle first comes to rest.[4]
  3. Find the total distance travelled in the first \(5\) seconds.[5]

Solution:

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Answer:\((a)\) Increasing cosine segment through \((0,-2)\), \((\pi,0)\) and \((2\pi,2)\). \((b)\) \(1.70\text{ s}\). \((c)\) \(4.41\text{ m}\).

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