Question

You compress a spring by a certain distance. then you decide to compress it further so that its elastic potential energy increases by another 50%. what was the percent increase in the spring's compression distance?

Answer 1

Elastic potential energy = 1/2 k * change of x^2
k- coefficient
x - change in length.
to increase energy 1.5 times you have to change x (compress) into $\sqrt{1.5}$  times (it's abot 1.22 or 22%)