Particle P moves along the y-axis so that its position at time t is given by y(t) = 4t - (2/3) for all times t. A second particle, particle Q, moves along the x-axis so that its position at time t is given by x(t) = (sin(πt))/(2-t) for all times t ≠ 2.
a) As time t approaches 2, what is the limit of the position of particle Q? Show the work that leads to your answer.
b) Show that the velocity of particle Q is given by v_Q(t) = (2πcos(πt) - πtcos(πt) + sin(πt))/((2-t)^2) for all times t ≠ 2.