Answer
The book slides away with a speed of 2.0 m/s
Work Step by Step
The book's kinetic energy when it slides away from the spring will be equal to the energy $U_s$ stored in the spring initially. We can find the speed of the book.
$KE = U_s$
$\frac{1}{2}mv^2=\frac{1}{2}kx^2$
$v^2=\frac{kx^2}{m}$
$v=\sqrt{\frac{kx^2}{m}}$
$v=\sqrt{\frac{(1250~N/m)(0.040~m)^2}{0.500~kg}}$
$v = 2.0~m/s$
The book slides away with a speed of 2.0 m/s.
