Four sets of qualitative graphs are described below. Each set lists a position–time graph (x–t), a velocity–time graph (v–t), and an acceleration–time graph (a–t). For which set could all three graphs represent the same one-dimensional motion?
(a) x–t: a parabola opening upward through the origin; v–t: a straight line with constant negative slope that begins at a positive velocity and crosses the time axis; a–t: a horizontal line at zero acceleration.
(b) x–t: a parabola opening upward that passes through the origin and becomes steeper with time; v–t: a straight line with constant positive slope beginning at v=0 when t=0; a–t: a horizontal line at a constant positive value.
(c) x–t: a parabola opening downward through the origin; v–t: a straight line with constant positive slope beginning at v=0; a–t: a horizontal line at a constant negative value.
(d) x–t: a straight line with constant positive slope; v–t: a horizontal line at a constant positive velocity; a–t: a horizontal line at a constant positive value.