Brakes
The Science of Stopping: It's All About Friction  Bicycle Brakes Convert Kinetic Energy (Motion) Into Thermal Energy (Heat).
Braking Distance
The approximate braking distance can be found by determining the work required to
dissipate the bike’s kinetic energy:
$\mathrm{work}=(\mu \times \mathrm{mass}\times \mathrm{gravity})\times \mathrm{distance}\phantom{\rule{0ex}{0ex}}\mathrm{kinetic}\mathrm{Energy}=\frac{1}{2}\times \mathrm{mass}\times {\mathrm{velocity}}^{2}$
Through the WorkEnergy Principle it can then be said that:
$(\mu \times \mathrm{mass}\times \mathrm{gravity})\times \mathrm{distance}=\frac{1}{2}\times \mathrm{mass}\times {\mathrm{velocity}}^{2}$Finally, by rearranging the equation and cancelling like terms we can form an equation for braking distance:
$\mathrm{distance}=\frac{{\mathrm{velocity}}^{2}}{(2\times \mu \times \mathrm{gravity})}$μ = coefficient of friction
Rim Brake

How's it Work?
Rubber pads are pressed against the rim of the wheel.

Advantages: inexpensive, lightweight, easy to maintain, mechanically
simple

Disadvantages: easily contaminated, less braking power
Disc Brake

How's it Work? Metallic or ceramic pads are pressed against a metal
rotor that's attached to the wheel.

Advantages: powerful, protected from contaminates, better heat dissipation
 Disadvantages: expensive, heavy, difficult to maintain