Dreams are created via our subconcious, so things that are held deep within our brains, not known to our concious mind (or forefront of our mind) come through whilst a sleep in images via dreams. people seem to think whilst we sleep we rest our minds, this is of course untrue, we only rest our conscious thought, our subconscious then can process all the information it has gathered through the day, week, month etc, this is then sometimes coverted into visual images, usually portrayed in metaphores.
eg if you are falling, this signifies being out of control, and you would probably feel you are not in control over something in your life.
if you are running away, this signifies you are running fron or avoiding something you can't conquere or feel you can't do.
if you are in an accident (like your hand brake accident) this signifies pent up guilt, or a change in your life that you couldn't control like bereavement, end of a relationship etc
this is all basically your subconcious connecting feelings and emotions with imagery, and obviously these sorts of feelings and emotions we all have in our lives, so often we have the same kind of dreams, this does not mean this is cast in stone but this is how we all process our thoughts and emotions when we sleep.
running when we are chased, is the same kind of feeling and emotion as being confronted with something we can't do, and have to constantly avoid or run away from, thus our subconcious connects the two via imagery and metaphor.
hope this helps you, and if you have a certain dream and want to try to understand it, try this site and type in the key parts of the dream in the interpret section.
http://www.dreammoods.com/
good luck, and sweet dreams!!