A particle moves in a straight line. Its velocity, \(v \mathrm{~ms}^{-1}\), at time \(t\) seconds is given by \(v=\cos t-\sin t\) (a) Find the acceleration, \(a \mathrm{~ms}^{-2}\), when \(t=\frac{\pi}{3}\).

The displacement of the particle from a fixed point \(O\) at time \(t\) is \(s\) metres. The particle passes through \(O\) when \(t=0\). (b) Find the displacement at the time when the particle first changes direction after passing through \(O\). (c) Find an expression for \(a\) in terms of \(s\).