A piece of wood floats in water kept in a beaker moves with a vertical acceleration a, the wood will

Remain in the same position relative to the water. We know when a wooden piece floats in a water kept in a beaker at rest we get  , when beaker is accelerated in vertically upward direction then we get $\text{m}\left(\text{g}+\text{a}\right)={\rho }_{\text{w}}\text{v}\left(\text{g}+\text{a}\right)$

We observe the volume of water displaced remain same so wooden piece remain in same position relative to water.