3. A force acting on a particle moving in the xy plane is given by F = 2yt + 1, where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.00 m and y = 5.00 m as shown in the figure. Calculate the work done by F on the particle as it moves along:
(a) the purple path
(b) the red path
(c) the blue path
(d) Is F conservative or nonconservative?
(e) Explain your answer to part (d).
Figure P731