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 \(s=\frac{10 t+100}{\sqrt{2 t^{2}+100}}\).
The diagram shows the displacement-time graph for the first 30 seconds of the motion.
(a) Find the value of \(t\) when \(s\) is a maximum.

(b) The particle passes through its starting point again at time \(t=T\).
(i) Find the total distance travelled by the particle during the first \(T\) seconds of its motion.

(ii) Use algebra to find \(T\).