2026 IGCSE Additional Mathematics May/June 0606/22 Q9

A particle \(P\) moves in a straight line such that \(t\) seconds after passing through a fixed point \(O\), its displacement from \(O\), \(s\) metres, is given by \(s=e^{4t}-10e^{2t}+9\).

1. The velocity of \(P\) is \(v\text{ m s}^{-1}\).
   Find the value of \(t\) for which \(v\) has a stationary value.[5]
2. Find the acceleration of \(P\) when \(t=\ln2\).[2]