Assiming that the driver can see and understand a hazard, they still eed the react safetly. The distance taken to stop has many factors: The reaction time of the driver, the quality of the breaks, the suract of the road. And most importantly, the speed of the vehicle. Reactions are slower to an unexpeced hazard than to an expected one. Other factors for reaction are age, tiredness, and the influence of drugs and alcohol.
Although the distence taken to have the reaction is proportional, the distance taken while breaking will be quadrupled. Travelling at 20mph will have a breaking distance of 6 metres whereas travelling at 40mph will have a breaking distance of 24 metres.
A high speed will reduce the change of the driver, firstly, noticing a hazard and, secondly, the reaction time and stopping distance once that hazard has been noticed.
It is often the case that in a traffic incident, the driver within the vehicle will fare better than the hazard that it has been collided with, be it a fence, cyclist of child. Pedestrians and cyclists will suffer more if the vehicle is travelling faster.