3
\includegraphics[max width=\textwidth, alt={}, center]{e060fc3b-ae93-46b5-b476-dcecb14d6d06-3_727_899_267_625} A boy runs from a point \(A\) to a point \(C\). He pauses at \(C\) and then walks back towards \(A\) until reaching the point \(B\), where he stops. The diagram shows the graph of \(v\) against \(t\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the boy's velocity at time \(t\) seconds after leaving \(A\). The boy runs and walks in the same straight line throughout.

1. Find the distances \(A C\) and \(A B\).
2. Sketch the graph of \(x\) against \(t\), where \(x\) metres is the boy's displacement from \(A\). Show clearly the values of \(t\) and \(x\) when the boy arrives at \(C\), when he leaves \(C\), and when he arrives at \(B\). [3]