In a vacuum, i.e. space, both objects would accelerate at the same rate. If the object they were attracted to was the same size as our planet the acceleration would be 9.81 m/s squared. In an atmosphere the acceleration would be inconsistent and based on air resistance.
The large mass can have proportionately more force applied to it than to the smaller mass.
Any amount of force, no matter how large or small, will increase or decrease the speed of any mass, no matter how large or small. But if you specify how much you want the object's speed changed and how quickly you want it done, then you have specified the acceleration you want. In that case, the larger the mass is, the more force it will take to accomplish that assignment.
an object's acceleration depends on the object's mass and the force applied to it. the lager the force applied to it.
Small object.
The difference is due to inertia. Inertia is the resistance to a change in motion (acceleration). A more massive object will have greater inertia, and therefore a greater resistance to a change in motion, resulting in a slower acceleration. A less massive object has lower inertia, and therefore less of a resistance to a change in motion, resulting in a faster acceleration.
Larger object.
the large object spreads the water out more evenly over it's area because it's large while the small object has less space to do so.
Acceleration due to gravity is the same for every object on or near Earth.
It's relative to what you define as a small object.
a larger object
Because of the large object has more surface area.
There is no specific force required to accelerate an object to a predetermined speed. A smaller force will produce a smaller acceleration, so it will take longer to reach the desired speed. A larger force will produce a larger acceleration, so the desired speed will be reached sooner. But either the large or the small force, or any other force, will produce an acceleration, and cause the object to reach the specified speed sooner or later.