How fast bicycle accelerate?

Answer 1

That's very dependent on the strength of the cyclist and the type of bicycle used.

Race BMXers are probably the fastest to reach their top speed, but track sprinters have a higher top speed. The way humans work and the way bicycles work means that full acceleration from standstill is rarely used, as a gear that makes for a good start will also mean a low top speed. And a gear that makes for a good top speed will make the bike sluggish at the start. Having a bike with multiple gears tends not to help that much, as very few shifting systems will work particularly well when shifting under full Power.

Answer 2

Either by the help of a downwards slope and gravity, or by the rider pedalling harder. Or possibly by encountering a strong tailwind.