The enegy E stored in an elastic band varies as the square of the extension x. When the elastic is extended by 3 cm, the energy stored when the extension is 5 cm ?

Question

Mercury · Answer

next time please post the full question: 
the energy E stored in an elastic band varies as the square of the extension x. when the elastic is extended by 3cm, the energy stored is 243 joules. what is the energy stored when the extension is 5 cm? What is the extension when the stored energy is 36 joules?

Mercury · Answer

as stated in the problem, E varies as the square of x

therefore E = kx^2, where k is some constant

it tells you that, when x = 3cm, E = 243. so you can plug in these x and E values and solve for k

- what is the energy stored when the extension is 5 cm? ---> use the E = kx^2 equation, plug in x = 5 and your k-value from before, then evaluate E

- What is the extension when the stored energy is 36 joules? ---> use the E = kx^2 equation, plug in E = 36 joules and your k-value, then solve for x