Answer
-22 $m/s^{2}$
Work Step by Step
We set up a system of linear equations:
$x = ut + \frac{1}{2}at^{2} $
$0 = (5800)t + \frac{1}{2}(-15)t^{2}$
$t(5800-\frac{15}{2}t)=0$
$t=0, t=\frac{2320}{3}$
$0 = (8600)t + \frac{1}{2}(a)t^{2}$
$t(8600+\frac{1}{2}at)=0$
$t=0, t=\frac{-17200}{a}$
$\frac{2320}{3}=\frac{-17200}{a}$
$2320a=-51600$
$a\approx-22\; m/s^{2}$
