Following up on AcousticAl...
With the exception of production dialog almost every other sonic element of a film is created in audio post. The spaces between lines of dialog are removed and replaced with room tone. Every footstep, body movement (cloth & skin), prop, etc. is performed and recorded by the Foley team. Everything from doors to vehicles to weapons to animals to the ambient atmosphere - and dozens of other things you would never think of - are all created (or pulled from libraries) and spotted by the sound effects team.
You can try to capture your "chase" sounds during production, but they will not have anywhere near the impact of those created in audio post, and you will not have anywhere near the amount of control you will need to create a compelling soundtrack.