Answer
At $s=75$ ft, $v=27.4$ ft /s
At $s=100$ ft, $v=37.4$ ft/s
Work Step by Step
$0\leq s < 100 $
$\int_0^v v dv = \int_0^s 5 ds$
$\frac{1}{2}v^2=5$ s
$v=\sqrt{10s}$
At $s=75$ ft, $v=\sqrt{750}=27.4$ ft /s
$v dv = a ds$
$\int_{31.623}^v v dv = \int_{100}^{125} [5 + 6(\sqrt{s} - 10)^\frac{5}{3}]ds$
$\frac{1}{2}v^2|^v_{31.623}=201.0324$
$v=37.4$ ft/s