The distance d that a spring will stretch varies directly as the force f applied to the spring. If a force of 6 lb is required to stretch the spring 3 in, what force is required to stretch the spring

The best answer i can think of is b

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. 

+10 that is always the common denominator

C. it comes from the core of the earth.