Answer
14 s
Work Step by Step
To find velocity when leaving the crossing:
$x=vt-\frac{1}{2}at^{2}$
$v=\frac{x+\frac{1}{2}at^{2}}{t}$
$v=\frac{20.0+\frac{1}{2}(1.6)(2.4)^{2}}{(2.4)}\approx10.2533$
Time required to reach 32 m/s:
$v=u+at$
$t=\frac{v-u}{a}=\frac{(32)-(10.2533)}{(1.6)}\approx14$ s
