[i]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, [/i][math]v[/math][math]ms^{-1}[/math][i] , at the [/i][math]t[/math][i] time instant after passing the fixed point P is given by [/i][math]v=6+4t-2t^2[/math][i] while Qian Hao runs with a constant velocity. Given the distance PQ is 50 m[br][Consider movement to the right is positive.][/i][br][br][i](a) Calculate Faiz's maximum velocity, in [/i][math]ms^{-1}[/math]

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

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

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