7 A vehicle is moving in a straight line. The velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t \mathrm {~s}\) after the vehicle starts is given by $$\begin{aligned} & v = A \left( t - 0.05 t ^ { 2 } \right) \quad \text { for } 0 \leqslant t \leqslant 15 ,
& v = \frac { B } { t ^ { 2 } } \quad \text { for } t \geqslant 15 , \end{aligned}$$ where \(A\) and \(B\) are constants. The distance travelled by the vehicle between \(t = 0\) and \(t = 15\) is 225 m .

1. Find the value of \(A\) and show that \(B = 3375\).
2. Find an expression in terms of \(t\) for the total distance travelled by the vehicle when \(t \geqslant 15\).
3. Find the speed of the vehicle when it has travelled a total distance of 315 m . \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. }