Greatest velocity and speed, distance before reversing, and whether a particle returns to its start

A particle travels along a straight line. Its velocity, \(v\text{ m s}^{-1}\), \(t\) seconds after it starts moving is given by \(v(t)=8+14t-4t^2\), for \(0\leq t\leq6\). The diagram below shows the graph of \(v\) against \(t\).

The graph has a local maximum point at \(t=\frac74\) and crosses the \(t\)-axis at \(t=4\).

1. Find the greatest value of the particle's
   1. velocity;
   2. speed.[4]

The particle changes its direction of motion when \(t=T\).

2. 1. Write down \(T\).
   2. Find the distance the particle travels from \(t=0\) to \(t=T\).[5]
3. Determine, with justification, whether the particle is ever back at its starting point for \(0<t\leq6\).[4]