[i]A particle moves along a straight line and passes a fixed point [/i][math]O[/math][i] with a velocity of [/i][math]-6ms^{-1}[/math][i] Its acceleration, [/i][math]a[/math][math]ms^{-2}[/math][i], at time [/i][math]t[/math][i] seconds after passing [/i][math]O[/math][i] is given by [/i][math]a=8-4t[/math][i].[/i][br][br][i][Assume movement to the right as positive.][/i][br][br][i](a) Find the maximum velocity, in [/i][math]ms^{-1}[/math][i] , of the particle.[/i]

[i](b) Find the time, in seconds, after the particle passes the fixed point [/i][math]O[/math][i] again.[/i]

[i](c) [/i][i]Sketch a velocity-time graph for the movement of the particle for [/i][math]0\le t\le3[/math][i].[/i]

[i](d) Next, find the total distance, in m, travelled by the particle in the first 3 seconds.[/i][br][br][br]