7 A particle \(P\) travels in a straight line from \(A\) to \(D\), passing through the points \(B\) and \(C\). For the section \(A B\) the velocity of the particle is \(\left( 0.5 t - 0.01 t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(t \mathrm {~s}\) is the time after leaving \(A\).

1. Given that the acceleration of \(P\) at \(B\) is \(0.1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find the time taken for \(P\) to travel from \(A\) to \(B\). The acceleration of \(P\) from \(B\) to \(C\) is constant and equal to \(0.1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. Given that \(P\) reaches \(C\) with speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the time taken for \(P\) to travel from \(B\) to \(C\).
   \(P\) travels with constant deceleration \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) from \(C\) to \(D\). Given that the distance \(C D\) is 300 m , find
3. the speed with which \(P\) reaches \(D\),
4. the distance \(A D\). \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. }