How fast can a cyclist accelerate from a standing start?
The power-drag equation is well-understood if not widely-known, and is discussed in this bicycles.SE answer. In particular, the drag equation shows the component for changes in kinetic energy, viz., acceleration. You're asking about a standing start, so initial speed is low and we can ignore the aerodynamic drag component. In addition, let's assume the rider and bicycle is on a flat surface, so we can also ignore the potential energy component. Finally, although there is a rolling and mechanical resistance component to drag, it is typically small so let's ignore it here.
What's left is the kinetic energy component. F = m a is the correct equation to use, but you have to convert F at the pedal to F available at the rear wheel. Then a = F / m. There are a series of lever arms between the pedal and the point at which the rear wheel touches the ground involving the length of the crank arm, the gear ratio, and the radius of the rear wheel. Let's say the total lever arm &quot;gain ratio&quot; is c. Then F Newtons of force at the pedal translate to F / c Newtons at the rear wheel. If the total mass of bike and rider is m, then the acceleration of the bike and rider is F / (m * c). Martin et al. (2006) uses this technique to model sprint performance, with very good results.
Maximum pedal force can actually be greater than body weight, if you can hold onto the handlebars. In fact, maximum pedal force approaches 1RM (&quot;1 rep max&quot;) force from a leg press. A world-class track sprinter has a 1RM of roughly 4x body mass; more commonly, most of us can produce pedal forces equivalent to at least twice body mass. So, depending on the gain ratio calculated above, maximum acceleration is likely to be somewhere in the ballpark of 0.2g to 0.4g, or between roughly 2 and 4 m/s^2.