Answer
The ball rolled a distance of 66.7 meters during the first 5.0 seconds.
Work Step by Step
Let $v_1$ be the velocity after 5.0 s and let $v_2$ be the velocity after 10.0 s.
$v_1 = (5.0~a)$ and $v_2 = (10.0~a)$
We can see that $v_2 = 2v_1$
During the second time interval of t = 5.0 s, the ball rolled a distance $d_2$ of 200 m.
$d_2 = (\frac{v_2+v_1}{2})(t) = \frac{3v_1}{2}(t)$
$v_1 = \frac{2d_2}{3t}$
We can use this expression to find $d_1$.
$d_1 = (\frac{v_1+v_0}{2})(t) = \frac{(2d_2)/(3t)}{2}~(t)$
$d_1 = \frac{d_2}{3} = \frac{200~m}{3} = 66.7~m$
The ball rolled a distance of 66.7 meters during the first 5.0 seconds.
