A block attached to an ideal spring is oscillating on a smooth...

In simple harmonic motion, the displacement of the block can be represented as $x = A \sin(\omega t)$.

The velocity of the block is the rate of change of displacement:
$v = \dfrac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin\left(\omega t + \dfrac{\pi}{2}\right)$

The restoring force exerted by the spring is directly proportional to the negative of displacement (Hooke's Law):
$F = -kx = -kA \sin(\omega t) = kA \sin(\omega t + \pi)$

Comparing the phase angles, the phase of velocity is $\left(\omega t + \dfrac{\pi}{2}\right)$ and the phase of the restoring force is $(\omega t + \pi)$.

The phase difference between the restoring force and the velocity is:
$\Delta \phi = \pi - \dfrac{\pi}{2} = \dfrac{\pi}{2} \text{ rad}$.

Answer: $\dfrac{\pi}{2} \text{ rad}$