2025 SST PRELIMS P2 Q11

2025 SST PRELIMS P2 Q11

Secondary 4
10 marks
2025 School of Science and Technology Prelims A Math Paper 2

A particle, travelling in a straight line, has velocity, \(v\) cm/s, given by \(v = 3t^2 - pt + 4\), where \(p\) is a constant and \(t\) seconds is the time after passing through a fixed point \(O\). The particle comes to instantaneous rest when \(t = 2\).

  1. Show that \(p = 8\).[1]
  2. Find the range of values of \(t\) during which the particle moves in the positive direction.[3]
  3. Find the minimum velocity of the particle.[3]
  4. Calculate the total distance travelled by the particle for the first 3 seconds.[3]

Solution:

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Answer:(i) \(p=8\) (ii) \(0\leq t<\frac{2}{3}\) or \(t>2\) (iii) \(-\frac{4}{3}\text{ cm s}^{-1}\) (iv) \(\frac{145}{27}\text{ cm}=5.37\text{ cm}\)

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