7 A motorcyclist starts from rest at \(A\) and travels in a straight line. For the first part of the motion, the motorcyclist's displacement \(x\) metres from \(A\) after \(t\) seconds is given by \(x = 0.6 t ^ { 2 } - 0.004 t ^ { 3 }\).

1. Show that the motorcyclist's acceleration is zero when \(t = 50\) and find the speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at this time. For \(t \geqslant 50\), the motorcyclist travels at constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find the value of \(t\) for which the motorcyclist's average speed is \(27.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }