On the diagram choose a location for a horizontal and vertical origin. label your choice with x=0 and y=0 on the diagram. choose a horizontal and vertical positive direction and label those directions on the diagram using arrows

Inelastic is the answer your looking for.

Ke reqd to move from 0 to 50 will be proportional to 50x50 or 2500. this is equal to w.  to change vel from 50 to 150 you need energy prop to 22500 - 2500 = 20,000. this corresponds to 8w.  best answer is a) . work reqd is prop to velocity squared.