2026 IGCSE Additional Mathematics February/March 0606/22 Q10

In this question time \(t\) is in seconds and displacement \(s\) is in metres.

For \(t\ge0\), a particle moves on the positive \(x\)-axis.

At time \(t\) the acceleration of the particle is \(2t-9\).

At time \(t=7\) the velocity of the particle is \(4\).

1. Find the times when the velocity of the particle is 0.[4]
2. At time \(t=12\), the displacement of the particle from the origin \(O\) is \(150\).
   1. Find an expression for the displacement of the particle at time \(t\).[3]
   2. Find the distance travelled by the particle in the first 6 seconds.[3]