2026 NORTHBROOKS P2 Q3

A computer animation shows a cartoon person walking in a straight line such that \(t\) seconds after it passes through a fixed point \(O\), its velocity, \(v\) cm/s, is given by \(v=pt-12t^2\), where \(p\) is a constant.

1. Given that the cartoon person attains a maximum walking speed at 2 seconds, show that \(p=48\) and hence find the maximum speed.[3]
2. Explain clearly why the total distance travelled by the person in the first 7 seconds is not obtained by finding the value of the displacement, \(s\), when \(t=7\).[2]
3. Find the total distance travelled by the person in the first 7 seconds.[4]