Question #42090

A wedge of angle $\theta = 45^\circ$ is forced to accelerate horizontally to the right with a time-varying acceleration $a(t) = kt$ ($k > 0$). A small block of mass $m$ rests on its rough inclined surface. The coefficients of static and kinetic friction between the block and the wedge are $\mu_s = 0.5$ and $\mu_k = 0.25$, respectively. Assuming the wedge's acceleration remains continuous, what is the magnitude of the sudden change in the vertical acceleration of the block at the exact instant it begins to slip? (Let $g$ be the acceleration due to gravity)