Question: Two particles move in the xy-plane. At time t, the position of particle A is given by x(t) = 4t - 4 and y(t) = 2t - k, and the position of particle B is given by x(t)=3t and y(t) = t2 - 2t - 1.
(a) If k = 5, do the particles ever collide? Explain.
(b) Find k so that the two particles do collide.
(c) At the time that the particles collide in part (b), which particle is moving faster?