Take \(g=10\,\mathrm{m\,s^{-2}}\). A particle moves in a straight line from a fixed point O. Its motion from \(t=0\) to \(t=T\) is modelled by four straight segments in the velocity-time graph. It accelerates from rest to \(V\,\mathrm{m\,s^{-1}}\) in 4 s, then decelerates at \(5/3\,\mathrm{m\,s^{-2}}\) to rest in 6 s. It travels back towards O, reaching a maximum speed of \(3\,\mathrm{m\,s^{-1}}\), before stopping at \(t=T\).

(a) Find V. [2]

(b) The total distance travelled is 68 m. Find T. [3]