Problem source

A particle is travelling in a straight line. 
It accelerates from its initial  velocity $u$  to
velocity $v$, where $v > \vert u \vert > 0\,$, travelling a distance $d_1$
with uniform acceleration of magnitude $3a\,$.  
It then comes to rest after travelling
a further distance $d_2\,$ with uniform deceleration of  magnitude $a\,$.
Show that
\begin{questionparts}
\item
if $u>0$ then $3d_1 < d_2\,$;
\item 
if $u<0$ then  $d_2 < 3d_1 < 2d_2\,$. 
\end{questionparts}

Show also that
 the average speed of the particle (that is,  the total distance
travelled divided by the total time)  is greater  in the case $u>0$ than  in the case $u<0\,$.
\noindent
{\bf Note:} In this question $d_1$ and $d_2$ are distances travelled by the particle which
are not the same, in the second case, as displacements from the starting point.