2026 NASS P1 Q13

A particle is travelling in a straight line. It passes a fixed point \(A\) with a velocity of \(-7\) m/s. Its acceleration, after passing \(A\) is given by \(a=8-2t\) for \(0\le t\le T\). On reaching its maximum speed at time \(T\) seconds, the particle begins to decelerate at a constant rate of \(1.5\) m/s\(^2\) until it comes to a rest at point \(B\).

1. Show that the particle first came to instantaneous rest when \(t=1\).[3]
2. Find the maximum velocity attained by the particle and the value of \(T\).[2]
3. Find the total distance travelled by the particle from \(A\) to \(B\).[4]