Answer
(a) We are moving south and slowing down.
(b) We are moving south at a constant velocity.
(c) We are at rest but speeding up toward the south.
(d) We are moving south and speeding up.
(e) It is not a good idea to use the expression "negative acceleration" to mean slowing down.
Work Step by Step
(a) $a_x \gt 0$ and $v_x \lt 0$
We are moving south and slowing down.
(b) $a_x = 0$ and $v_x \lt 0$
We are moving south at a constant velocity.
(c) $a_x \lt 0$ and $v_x = 0$
We are at rest but speeding up toward the south.
(d) $a_x \lt 0$ and $v_x \lt 0$
We are moving south and speeding up.
(e) Negative acceleration means $a_x \lt 0$. If $v_x \gt 0$, then we would be slowing down. However, if $v_x \lt 0$, then we would not be slowing down; we would be speeding up in the negative direction.
In answer (a), the acceleration is positive but we are slowing down. In answers (c) and (d), the acceleration is negative, but we are speeding up in both cases.
Therefore, it is not a good idea to use the expression "negative acceleration" to mean slowing down.
