(B) Object $B$.
$(b)$ No,all three objects $A$,$B$,and $C$ never meet at a single point on the graph.
$(c)$ To find the distance $C$ has travelled when $B$ passes $A$:
$1$. Identify the point where $B$ and $A$ intersect. This occurs at a distance of $9 \, km$ from the origin.
$2$. At this time,look at the position of object $C$ on the graph. Object $C$ is at a distance of approximately $7 \, km$ from the origin.
$3$. Object $C$ started at $2 \, km$ from the origin.
$4$. Therefore,the distance travelled by $C$ is $7 \, km - 2 \, km = 5 \, km$.
$(d)$ To find the distance $B$ has travelled by the time it passes $C$:
$1$. Identify the point where $B$ and $C$ intersect. This occurs at a distance of approximately $9.14 \, km$ from the origin.
$2$. Since object $B$ started from the origin $(0 \, km)$,the distance travelled by $B$ is $9.14 \, km - 0 \, km = 9.14 \, km$.