Can someone help please with this Physics question?

Question

A glider of mass 0.250 kg moves on a horizontal frictionless airtrack. It is permanently attached to one end of a massless horizontal spring, which has a force constant of 13.0 N/m both for extension and for compression. The other end of the spring is fixed. The glider is moved to compress the spring by 0.180 m and then released from rest.

(a) Calculate the speed of the glider at the point where it has moved 0.180 m from its starting point, so that the spring is momentarily exerting no force.
(b) Calculate the speed of the glider at the point where it has moved 0.250 m from its starting point.

Answer 1

I like to use energy to solve these types of problems.

The energy in a spring is
1/2*k*x^2
the kinetic energy of a mass is
1/2 m*v^2

a)
m*v^2=k*x^2
v=sqrt(k*x^2/m)
=sqrt((13*.18^2)/.25)
=1.3 m/s

at .250 m
.25*v^2=.25*1.3^2-13*(.25-.18)^2
v^2=1.3^2-4*13*(.25-.18)^2
v=sqrt(1.3^2-4*13*(.25-.18)^2)
=1.2 m/s

j