Question

what variables affect the acceleration of an object and in what matter do they affect the acceleration?

Answer 1

The variables that affect the acceleration of an object are

-- the object's mass
and
-- the net force acting on the object.

Acceleration = (net force) divided by (mass) .

The more mass an object has, the less acceleration it will have
in response to the same net force.

The more net force acts on an object, the more acceleration
the object will have.