Answer
The cart must have an acceleration of $\frac{g}{\mu_s}$ so the block does not fall. An observer on the cart would say that the block is at rest.
Work Step by Step
Let $m$ be the mass of the block. If the block does not fall, then the force of static friction directed up must be equal in magnitude to the weight of the block.
$F_N~\mu_s = mg$
$F_N = \frac{mg}{\mu_s}$
We can use the normal force $F_N$ between the cart and the block to find the acceleration of the block.
$\sum F = ma$
$F_N = ma$
$\frac{mg}{\mu_s} = ma$
$a = \frac{g}{\mu_s}$
The cart and the block must have the same acceleration. The cart must have an acceleration of $\frac{g}{\mu_s}$ so the block does not fall. An observer on the cart would say that the block is at rest.
