Sometimes reactions to stimuli seem immediate, but in reality they always take time. A short period of time, perhaps, but still time, and while that time passes, events around us continue to occur. In the case of a driver who needs to stop a vehicle, during the three-quarters of a second that it takes for nerve messages to travel from eye to brain to leg muscles to begin the braking, the vehicle continues to move at its original speed. If the original speed is 20 miles per hour, then 22 feet are traveled before braking even begins.

The faster the vehicle moves, the more distance is traveled during reaction time. For example, if the vehicle is traveling 40 miles/hour on a road instead of 20 miles/hour in a parking lot, then it travels 44 feet between the visual stimulus and the muscle reaction.

After the driver applies the brakes, the time it takes to stop depends on a number of factors such as brake quality, tire tread, and road conditions. However, stopping distance depends most on the speed of the vehicle.

The higher the vehicle’s speed, the higher its kinetic energy, a form of mechanical energy. Since kinetic energy = ½ x mass x velocity², increasing the speed causes an exponential increase in mechanical energy of the vehicle; doubling the speed causes a fourfold increase in mechanical energy, and tripling causes a ninefold increase.

When braking, the mechanical energy of the vehicle transforms into other types of energy, predominantly thermal energy. Stopping the vehicle means transforming all of its mechanical energy so that none remains, and doing so requires doing “work” on the vehicle.

According to the work-energy principle, work done on an object = the change in kinetic energy of the object.

If the vehicle slows to a stop, then final kinetic energy = 0, so change in kinetic energy is simply the negative of the initial kinetic energy.

If given that a vehicle going 20 miles/hour takes 20 feet to stop once brakes are applied, then the same vehicle going 40 miles/hour in similar circumstances requires 80 feet to stop, and at 60 miles/hour, 180 feet.

Combine these braking distances with the distance traveled during reaction time, and the total stopping distance is surprisingly long.

To learn more about speed and distance, check out Calculating Speed, To Survive at High Velocity and Virtual Car: Velocity and Acceleration.

To learn more about the brain and how it works, check out Brain Geography.

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