2025 IGCSE Additional Mathematics February/March 0606/22 Q9

2025 IGCSE Additional Mathematics February/March 0606/22 Q9

11 marks

In this question, all lengths are in metres and time is in seconds.

A particle, \(P\), moves in a straight line such that \(t\) seconds after passing through a fixed point \(O\) its displacement, \(s\), is given by \(s=5\ln(2t+1)-5t\).

  1. Find the value of \(t\) for which \(P\) is instantaneously at rest.[4]
  2. Find the distance \(P\) travels between \(t=0\) and \(t=2\).[4]
  3. Find an expression for the acceleration of \(P\) in terms of \(t\).[2]
  4. Find the acceleration when \(t=4.5\).[1]

Solution:

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Answer:(a) \(t=0.5\text{ s}\) (b) \(3.88\text{ m}\) (c) \(-\dfrac{20}{(2t+1)^2}\text{ m s}^{-2}\) (d) \(-0.2\text{ m s}^{-2}\)

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