A walker travels along a straight road passing through the points A and B on the road with speeds 0.9 m s^-1 and 1.3 m s^-1 respectively. The walker’s acceleration between A and B is constant and equal to 0.004 m s^-2.

1. Find the time taken by the walker to travel from A to B, and find the distance AB.

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 s after leaving A the cyclist’s speed is kt³ m s^-1, where k is a constant.

1. 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.
2. Find the cyclist’s acceleration at the instant she passes through B.