necessary data
1 mass of object
2 fraction between mass and floor
3 how much time the force will be applied
4 the diagram of force-time or probability density of that diagram( to find mean value and standard deviation) but for more precise solution the diagram would be good.
5 G
6 the angle between the force vector and object
7 the cohesion between hand and object
8 the air pressure of environment also shape of object to calculate the boundary conditions of air.
9 the place of the experiment to calculate the centrifugal effect of earth.
bla
bla
bla
in conclusion you cant know the exact acceleration unless you have an enormous data. i can only tell you the possibilities.