Answer
(a) Case 3 and case 4.
(b) Case 2.
(c) Case 2 and case 3.
Work Step by Step
(a) In cases 3 and 4 the starting position is positive and $a\lt0$. If $v_0\gt0$ (case 3), the ball starts moving in the positive direction, but is decelerating. So, the ball will stop and change its direction and, finally, will cross $x=0$. If $v_0\lt0$ (case 4), the ball starts moving in the negative direction and accelerating. The ball will cross $x=0$.
(b) In case 2 the starting position is positive, $v_0$ is negative and $a$ is positive. So, the ball is decelerating and will stop before changing its direction (from negative to positive direction). The question is: "Will the ball change the direction before or after pass $x=0?$"
(c) In the cases in which $v_0$ and $a$ point in opposite directions, cases 2 and 3.
