Final answer:
The closest given option is d. 1.0 m, but the correct answer based on the calculation should be slightly less than 0.674 m.
Step-by-step explanation:
To determine how far you must stretch a spring with a force constant k = 1100 N/m to store 250 J of energy, you can use the formula for the potential energy stored in a spring, which is PE = 1/2 k x2, where PE is the potential energy, k is the spring constant, and x is the displacement from the spring's equilibrium position. Solving this equation for x when PE = 250 J, we get:
x = √(2*PE/k) = √(2*250J/1100N/m) = √(500/1100) meters = √(0.4545) meters ≈ 0.674 m
This value is not listed among the options, so there might be a misunderstanding in the question as presented or a typo in the given answers. To find the displacement needed to store 250 J of energy in a spring with a force constant of 1100 N/m, use the potential energy formula. The calculation yields a value of approximately 0.674 m, none of the provided options match this result, indicating a potential error in the question.