2024 FMSS PRELIMS P2 Q10

A particle moves in a straight line such that, \(t\) s after passing through a fixed point \(O\), its displacement from \(O\) is \(s\) m. The velocity \(\mathrm{v}\) ms\(^{-1}\) of the particle is such that \(\mathrm{v} = 6\cos{4t}\)

1. State the initial velocity of the particle.[1]
2. Find the first value of \(t\) when the acceleration of the particle is equal to \(8\text{ ms}^{-2}\).[2]
3. Find the displacement of the particle from \(O\) when \(t = 4\).[3]
4. Find the total distance travelled by the particle for the first \(\frac{3\pi}{8}\) seconds.[5]