Answer
(a) $a_x \lt 0 $ at $t_3$ and $t_4$.
(b) $a_x = 0$ at $t_0$, $t_2$, $t_5$, and $t_7$.
(c) $a_x \gt 0 $ at $t_1$ and $t_6$.
(d) $v_x = 0 $ at $t_0$, $t_3$, and $t_7$.
(e) The speed is decreasing at $t_6$.
Work Step by Step
(a) The slope of the position versus time graph is the velocity. If the slope is becoming more negative or less positive, then $a_x \lt 0$. On the graph, we can see that $a_x \lt 0 $ at $t_3$ and $t_4$.
(b) The slope of the position versus time graph is the velocity. If the slope is constant then $a_x = 0$. On the graph, we can see that $a_x = 0$ at $t_0$, $t_2$, $t_5$, and $t_7$.
(c) The slope of the position versus time graph is the velocity. If the slope is becoming more positive or less negative, then $a_x \gt 0$. On the graph, we can see that $a_x \gt 0 $ at $t_1$ and $t_6$.
(d) The slope of the position versus time graph is the velocity. On the graph, we can see that $v_x = 0 $ at $t_0$, $t_3$, and $t_7$.
(e) The slope of the position versus time graph is the velocity. If the graph is becoming less steep, that is less positive or less negative, then the speed is decreasing. On the graph, we can see that the speed is decreasing at $t_6$.
