Meaning of dreaming of running fast depends on situation as per dream interpretation. People usually dream of running fast when they are sacred or fed up with current life. The dream is asking you to not to indulge in bad activities and it is asking you to do positive things. To those who are fed up with current life, it is asking you to take the plunge and start exploring new things. This running is for freedom.
Seeing dream of running fast and someone behind chasing you means you will face problems from authorities. You should be prepared to get exposed if you have done something wrong.
Dreaming of you running fast and going across other people means that you will score victory over enemies. You will overcome a difficult situation.
Dreaming of running fast and you falling means a work in near future will be destroyed due to carless and hastiness. You need to show patience and keep a calm mind.
Dreaming of running fast and looking back means you will do some action that will cause embarrassment and shame to family. So be careful about activities in near future.