Springs, kinetic energy and work

[eprparadox]

Homework Statement

A 2 kg block is attached to a horizontal ideal spring with a spring constant of 200 N/m. When the spring has its equilibrium length the block is given a speed of 5 m/s. What is the maximum elongation of the spring?

A. 0
B. 0.05 m
C. 5 m
D. 10 m
E. 100 m

Homework Equations

Conservation of Energy: E(initial) = E(final)
1/2*m*vi^2 + 1/2*k*xi^2 = 1/2*m*vf^2 + 1/2*k*xf^2

The Attempt at a Solution

At the point where it has a speed of 5 m/s there is only kinetic energy and at max elongation there is only potential energy. So I set 1/2*2*5^2 = 1/2*200*x^2 and I solved for x and I got 0.5 m.

This isn't one of the choices so I'm not sure if I'm doing this incorrectly or if there is an error in the problem.

Thanks ahead of time for any help.

 

[Doc Al]

At the point where it has a speed of 5 m/s there is only kinetic energy and at max elongation there is only potential energy. So I set 1/2*2*5^2 = 1/2*200*x^2 and I solved for x and I got 0.5 m.

Your solution is correct.