The diagram above shows the position and direction of motion of two boys, Faiz and Qian Hou who are running on a straight path and each passes through two fixed points, P and Q. At the time Faiz passes through the fixed point P, Qian Hao passes through the fixed point Q. Faiz stops for a moment at point R. Faiz's velocity, [math]v[/math][math]ms^{-1}[/math] , at the [math]t[/math] time instant after passing the fixed point P is given by [math]v=6+4t-2t^2[/math] while Qian Hao runs with a constant velocity .[br]Given the distance PQ is 50 m[br][br][Consider movement to the right is positive.][br][br](a) Calculate Faiz's maximum velocity, in [math]ms^{-1}[/math]

[br](b)(i) Sketch the velocity-time graph of Faiz from point P to point R.

[br] (ii) Next, find the distance Faiz, in m, from point P to point R

[br](c) Determine the distance, in m, between Faiz and Qian Hao when Faiz is at point R.