1 A car travels in a straight line with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). It passes the points \(A , B\) and \(C\), in this order, with speeds \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 } , 7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The distances \(A B\) and \(B C\) are \(d _ { 1 } \mathrm {~m}\) and \(d _ { 2 } \mathrm {~m}\) respectively.

1. Write down an equation connecting
   (a) \(d _ { 1 }\) and \(a\),
   (b) \(d _ { 2 }\) and \(a\).
2. Hence find \(d _ { 1 }\) in terms of \(d _ { 2 }\).