Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 6

At \( t = 0 \), a particle moving along an \( x \) axis is at position \( x_0 = -20 \text{ m} \). The signs of the particle's initial velocity \( v_0 \) (at time \( t_0 \)) and constant acceleration \( a \) are, respectively, for four situations: (1) \( +, + \); (2) \( +, - \); (3) \( -, + \); (4) \( -, - \). In which situations will the particle (a) stop momentarily, (b) pass through the origin, and (c) never pass through the origin?