Two particles move in the $xy$-plane. At time $t$, the position of particle $A$ is given by $x(t) = 3 t - 3$ and $y(t) = 3 t - k$, and the position of particle $B$ is given by $x(t) = 2 t$ and $y(t) = t^2 - 2t - 1$.

(a) If $k = 5$, do the particles ever collide?
A. yes
B. no
C. it is not possible to determine for certain

(Be sure that you are able to explain your answer!)

(b) Find $k$ so that the two particles are certain to collide.
$k =$

(c) At the time the particle collide in (b), which is moving faster?
A. particle A
B. particle B
C. neither particle (they are moving at the same speed)