2024 IGCSE Additional Mathematics October/November 0606/21 Q8

A particle moves in a straight line so that its displacement from a fixed point \(O\) at time \(t\) seconds is \(x\) metres, where \(x=t^3+t^2-t+8\) and \(t\geq0\).

1. Find the time when the particle changes direction.[3]
2. Show that the particle is moving towards \(O\) when \(t=0\).[3]
3. Find the total distance travelled by the particle during the first 2 seconds of its motion.[4]