Block on an inclined plane with Coulomb friction

What you are seeing: a block of mass $m$ on a slope of angle $\theta$, with static friction $\mu_s$ and kinetic friction $\mu_k$. The block sits still until $\tan\theta$ exceeds $\mu_s$, then breaks free and accelerates at constant $a = g(\sin\theta - \mu_k \cos\theta)$. Below threshold the slider just confirms equilibrium: static friction silently rises to match the component of gravity along the slope.

Two diagnostic curves on the right track the block's velocity in time and the analytic prediction $v(t) = a\,t$. Once the block moves, the numerical trajectory tracks the analytic curve to machine precision (velocity-Verlet is exact for constant acceleration).