7 A walker travels along a straight road passing through the points \(A\) and \(B\) on the road with speeds \(0.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(1.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The walker's acceleration between \(A\) and \(B\) is constant and equal to \(0.004 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find the time taken by the walker to travel from \(A\) to \(B\), and find the distance \(A B\). A cyclist leaves \(A\) at the same instant as the walker. She starts from rest and travels along the straight road, passing through \(B\) at the same instant as the walker. At time \(t \mathrm {~s}\) after leaving \(A\) the cyclist's speed is \(k t ^ { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(k\) is a constant.
2. Show that when \(t = 64.05\) the speed of the walker and the speed of the cyclist are the same, correct to 3 significant figures.
3. Find the cyclist's acceleration at the instant she passes through \(B\).