What two factors affect the rate of acceleration of an object?

For help with this answer, we look to Newton's second law of motion:

     Force = (mass) x (acceleration)

Since the question seems to focus on acceleration, let's get
'acceleration' all alone on one side of the equation, so we can
really see what's going on.

Here's the equation again:

                                                 Force = (mass) x (acceleration)

Divide each side by 'mass',
and we have:                            Acceleration = (force) / (mass) .

Now the answer jumps out at us:  The rate of acceleration of an object
is determined by the object's mass and by the strength of the net force
acting on the object.