How do things accelerate when there is no air present?

Answer 1

Air is not a requirement for acceleration. Objects in the vacuum of space accelerate to other objects under the force of gravitational attraction. Rockets are propelled by escaping gases in the same manner as you are accelerated in the opposite direction when you throw an object while you are sitting on a rolling chair.

Answer:

Let's look at the case of an object falling from a great height towards the Earth.

Once the object is released it accelerates towards the Earth due to gravity at 32ft/sec/sec. The acceleration continues until the force required to push through the air balances the force of gravity . This is known as terminal velocity.

Now lets consider an airless planet the same size as Earth (to make the attraction of gravity the same). We drop the body from the same height over its surface, it accelerates downward, but does not have to push air out of the way. There is no terminal velocity ands its speed continues to increase all the way to the ground.

Thus bodies falling through a gas accelerate until terminal velocity is reached, bodies falling in a vacuum continue to accelerate.