2024 IGCSE Additional Mathematics October/November 0606/23 Q12

A particle moves in a straight line. Its velocity, \(v\text{ m s}^{-1}\), at time \(t\) seconds is given by \(v=\cos t-\sin t\).

1. Find the acceleration, \(a\text{ m s}^{-2}\), when \(t=\dfrac\pi3\).[2]

The displacement of the particle from a fixed point \(O\) at time \(t\) is \(s\) metres. The particle passes through \(O\) when \(t=0\).

2. Find the displacement at the time when the particle first changes direction after passing through \(O\).[6]
3. Find an expression for \(a\) in terms of \(s\).[1]