I am considering building an iPhone GPS app to assist runners. It would need to get an accurate speed reading (within 1mph) every 10 seconds. Is the iPhone 3GS or the new iPhone 4 capable of giving a reading this accurate?
In terms of accuracy it's possible (as long you don't lose the signal of course). Especially since GPS is much more accurate in relative positioning (i.e. it might have 10m uncertainty in positioning you on the map, but it'll detect it if you move for 1m). For periods that there's no signal, you'll just get an average velocity or something.
However note that leaving the GPS on like this will dramatically eat up the battery so it might not be very satisfactory for your customers if used for a long period.
You might want to use other technologies or ask for the user's assistance and use the GPS less often. For example, you could sample the location every minute or so, and then use the map API to guess how the user moved from A to B (or ask the user if it's not possible).
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