(a) The diagram shows the displacement-time graph of a particle \(P\). On the axes provided, draw the velocity-time graph of \(P\).

(b) A particle \(Q\) moves in a straight line such that its velocity, \(v\text{ m s}^{-1}\), \(t\) seconds after passing through a fixed point \(O\), is given by \(v=3e^{-5t}+\dfrac32t\), for \(t\geq0\).

(i) Find the velocity of \(Q\) when \(t=0\).

(ii) Find the value of \(t\) when the acceleration of \(Q\) is zero.

(iii) Find the distance of \(Q\) from \(O\) when \(t=0.5\).