How can more speed increase braking distance?
The type of energy that keeps an object in motion is called "kinetic energy." This motion may mean bouncing, whirling in circles, vibrating, whatever - if something is moving, it is displaying kinetic energy in that movement. If two objects are moving at the same speed but one has twice as much mass as the second, the object with more mass will display more kinetic energy - it will take a longer period of time for it to stop moving if the energy is not restored to either object.
An object that is moving fast takes a longer distance to stop moving than one that is moving slowly for the same reason. The kinetic energy level of a moving vehicle increases as the speed with which the vehicle is moving increases. The increased level of kinetic energy will require an increased distance to transform to other types of energy (much of it will become thermal energy due to friction when braking) as the vehicle comes to a halt.