According to a study performed in 1997 by Texas A&M University for the Transportation Research Board of the National Research Council (available at their website
) people driving at night using low-beam headlights cannot see a large animal like a deer at a distance of anywhere from about 80 m to 100 m (see the figure above taken from NCHRP Report #400). Another study performed in 1998 by the U.S. Army for the Department of Transportation's National Highway Traffic Safety Administration indicated that 43 m is a good braking distance for a sedan with anti-lock brakes traveling at 100 km/h and 50 m is a poor braking distance. If you were driving down the highway at 100 km/h at night using your low-beam headlights, how much time do you have to react to an animal in the road, assuming you notice it at a distance of 95 m and your car has a braking distance of 43 m? In other words, how much time can elapse between the instant you first spot the animal and the instant you hit the brakes without resulting in an accident?
System: Your car will be treated as a point particle.
Model: [One-Dimensional Motion with Constant Velocity]. Although the car will eventually stop, we are interested in the time that elapses from the instant the animal is recognized until the instant the brakes are pressed. During that time interval, the car is coasting at 100 km/h.
Approach: Our model has only one relevant Law of Change, namely:
\begin
[ x = x_
+ vt] \end
To use it properly in this case, however, requires consideration of the meaning of the givens. We are looking for the time, and the velocity is clearly 100 km/h, but we run into some trouble with the position values. The equation only involves two positions, but we are given five quantities with units of meters.
To determine which positions to use, it is helpful to sketch the situation. The important information in the problem statement can be summarized as shown below.
