2025 DSS PRELIMS P1 Q27

The diagram shows the speed-time graph for two cyclists, \(A\) and \(B\), travelling along the same track in the same direction. \(A\) travels at a constant speed of \(5\text{ m/s}\) for 10 seconds and then decelerates to a stop at \(T\) seconds. \(B\) travels at a constant speed of \(3\text{ m/s}\) for 8 seconds and then accelerates till \(T\) seconds. When \(t=10\), the speed of \(B\) is \(5\text{ m/s}\).

1. Calculate the acceleration of \(B\) after 8 seconds.[1]
2. The area beneath each speed-time graph represents the distance travelled by each cyclist.
   1. Find an expression, in terms of \(T\), for the distance travelled by \(A\) in the \(T\) seconds.[1]
   2. When \(t=0\), both \(A\) and \(B\) start at the same position. When \(t=T\), both \(A\) and \(B\) meet again. Form an equation to represent this information and show that it simplifies to \(T^2-15T+14=0\).[3]
   3. Solve the equation and find the value of T.[2]