Two particles move in the xy-plane. For time t >= 0, the position of particle A is given by x = t - 2 and y = (t - 2)^3, and the position of particle B is given by x = (3t/2) - 1 and y = (3t/2) + 2.
1) Set up the integral expression that gives the distance traveled by particle A from t = 0 to t = 3.
2) Determine the exact time at which the particles collide; that is, when the particles are at the same point at the same time.
3) Sketch the paths of particles A and B from t = 0 until they collide. Indicate the direction of each particle along the path.