How does kinetic energy affect the stopping distance of a vehicle traveling at 30 mph compared to the same vehicle traveling 60 mph

The more kinetic energy an object has, the larger velocity it has if the mass holds constant. Therefore, unless the stopping force is larger for a vehicle of higher kinetic energy with the same mass, than under constant acceleration, the stopping distance of a vehicle traveling at higher velocities would be greater than the stopping distance of a vehicle traveling at lower velocities. 

Mathematically, if we call the deceleration  and the time to decelerate for the car traveling at 30mph is , than , than it is obvious that the 60mph car requires , therefore the deceleration would total . Using a kinematic equation, we see that .

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