You are traveling along a road at 90 km/hr, maintaining a constant distance d be

Question

You are traveling along a road at 90 km/hr, maintaining a constant distance d between you and the car in front of you, measured from your front bumper to the other car's rear bumper.
(a) If the driver of the car in front of you applies the brakes to come to a complete stop, what is the minimum value of d required if you are not to hit the other car? Assume your reaction time (the time it takes you to see the brake lights in front and apply your own brakes) is 0.38 s and that the appropriate coefficient of friction between the road and your car tires is 0.85. Assume the acceleration due to gravity has a magnitude of 9.8 m/s2.

Explanation / Answer

Since you and the car in front of you have the same acceleration when you kit the brakes, the minimum distance is the one you need so that you hit your brakes right at the point that he hit his brakes at. Since that might be a little confusing, look at it this way, the car in front will take some distance L to stop. You will take the same distance, plus however much you travel in the time it takes you to react, so L + r. Since you are behind the car, you will just barely stop on their bumper if the distance you are behind the car is r. Then, the minimum distance is the amount you travel in the time it takes you to react. 90 km/hr=0.025km/sec then multiply by .38 to get .0095Km or 9.5m

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