Po 2. A laser is a device that produces a beam of light. A design, shown above, is etched onto a flat piece of metal using a moving laser. The position of the laser at time / seconds is represented by (x(1), y(t)) in the xy-plane. Both x and y are measured in centimeters, and is measured in seconds. The laser starts at position (0, 0) at time 1 = 0, and the design takes 3.1 seconds to complete. For 0 S1 3.1. =3 cos (1) and dy dt = 4 cos (2.51). 2. A laser is a device that produces a beam of light. A design, shown above, is etched onto a flat piece of metal using a moving laser. The position of the laser at time t seconds is represented by (x(1), y(t)) in the xy-plane. Both x and y are measured in centimeters, and t is measured in seconds. The laser starts at position (0,0) at time f = 0, and the design takes 3.1 seconds to complete. For 0 st 3.1. = 3 cos () and dx dt dt = 4 cos (2.5t). (a) Find the speed of the laser at time t = 3 seconds. (b) Find the total distance traveled by the laser from time t = 1 to time t = 3 seconds. (c) The laser is farthest to the right at time t= 1.253 seconds. Find the x-coordinate of the laser's rightmost position. (d) What is the difference between the y-coordinates of the laser's highest position and lowest position for 0 SIS 3.1? Justify your answer.