Answer
$t=\pm\sqrt{\dfrac{2(r-r_{0})}{a}}$
Work Step by Step
$r=r_{0}+\dfrac{1}{2}at^{2}$, for $t$
Multiply the whole equation by $2$:
$2\Big(r=r_{0}+\dfrac{1}{2}at^{2}\Big)$
$2r=2r_{0}+at^{2}$
Rearrange:
$2r_{0}+at^{2}=2r$
Take $2r_{0}$ to subtract the right side:
$at^{2}=2r-2r_{0}$
Take $a$ to divide the right side:
$t^{2}=\dfrac{2r-2r_{0}}{a}$
Take the square root of both sides:
$\sqrt{t^{2}}=\pm\sqrt{\dfrac{2r-2r_{0}}{a}}$
$t=\pm\sqrt{\dfrac{2r-2r_{0}}{a}}$
Take out common factor $2$ from the numerator inside the square root to show a better looking answer:
$t=\pm\sqrt{\dfrac{2(r-r_{0})}{a}}$
