Answer
The cart was moving with a speed of 3.0 m/s just before it hit the spring.
Work Step by Step
The cart's kinetic energy just before it hit the spring is equal to the energy $U_s$ stored in the spring after the spring is compressed by 60 cm. We can find the speed of the cart just before it hit the spring. Therefore;
$KE = U_s$
$\frac{1}{2}mv^2=\frac{1}{2}kx^2$
$v^2=\frac{kx^2}{m}$
$v=\sqrt{\frac{kx^2}{m}}$
$v=\sqrt{\frac{(250~N/m)(0.60~m)^2}{10~kg}}$
$v = 3.0~m/s$
The cart was moving with a speed of 3.0 m/s just before it hit the spring.
