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