2025 IGCSE Additional Mathematics October/November 0606/23 Q10

In this question the units are metres and seconds.

A particle moves along a straight line through a point \(A\).

Its displacement, \(s\), from \(A\) at time \(t\) is given by \(s=\dfrac{10t+100}{\sqrt{2t^2+100}}\).

The diagram shows the displacement–time graph for the first 30 seconds of the motion.

1. Find the value of \(t\) when \(s\) is a maximum.[6]
2. The particle passes through its starting point again at time \(t=T\).
   1. Find the total distance travelled by the particle during the first \(T\) seconds of its motion.[2]
   2. Use algebra to find \(T\).[3]