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

a) 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 ts after leaving $A$ the cyclist’s speed is $k{t^3}{\text{ }}m{\text{ }}{s^{ - 1}}$, where $k$ is a constant.

b) 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.

c) Find the cyclist’s acceleration at the instant she passes through $B$.