Achieving supersonic speeds on a bicycle is a highly challenging task due to various aerodynamic, structural, and safety considerations. While it's theoretically possible to attach jet engines to a bicycle, it would require an enormous amount of power, engineering expertise, and specialized materials to withstand the extreme forces involved.
To break the sound barrier (approximately 1,225 kilometers per hour or 761 miles per hour at sea level), you would need significantly more power than what can be generated by jet engines typically used on aircraft. Jet engines on commercial airliners produce a maximum thrust of tens of thousands of pounds, while the speed of sound requires sustained thrust in the hundreds of thousands or even millions of pounds range.
Moreover, the aerodynamic design of a bicycle is not optimized for high-speed flight, which would result in instability, control issues, and potentially catastrophic failure. The bicycle frame, wheels, and other components are not designed to handle the forces and stresses associated with supersonic speeds.
In summary, the task of achieving supersonic speeds on a bicycle is currently beyond our technological capabilities, and it would require advancements in materials, power generation, and aerodynamics to even consider such an endeavor.