May/June 2026 Paper 43

A train is travelling along a straight track with constant acceleration $am/{\mathrm{s}}^2$. It passes through points $A$, $B$ and $C$ on the track in that order. The distances $AB$ and $BC$ are $280\mathrm{m}$ and $170\mathrm{m}$ respectively. The speed of the train at $B$ is $32m/s$. The time it takes the train to travel from $A$ to $B$ is $2t\mathrm{s}$ and from $B$ to $C$ is $t\mathrm{s}$. Find the value of $a$ and the value of $t$.