The Crash Test

One you want to be smart enough to avoid

by James Brevard at Klein Oak High School

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Ever been in a car and some jerk cut you off? Well, how deep was the cut? Understanding velocity and friction can help us figure out how much space to keep in front of us.


Use the Web search engines to find information about our problem. What we need is data about braking distances and human reaction time. The experience of others is good, and I'm sure your search will find answers to our problem, but what we want is some "raw" data that we can analyze for ourselves.


Answer the following questions. The car is moving at 35 mph.

  1. What is a reasonable value for human reaction time?
  2. How far will the car travel during that amount of time?
  3. What average distance is needed for the car to stop once the brakes have been applied?
  4. Using your formula, V^2=Vo^2+2ad, calculate the acceleration of the car.
  5. Using a graphing calculator, plot a position/time graph for both cars on the same display.

    The formula to enter for Y1 AND Y2 is d=So + (Vo)t + (1/2)at^2.<> For the trailing car, So = 0.

    For the leading car, So = a guess by YOU!

    Convert 35 mph into m/s and enter that value for Vo.

    The value for "a" is what you calculated for #4, but be sure that you enter it as a NEGATIVE number.

    Your "X variable" is "t".

    Experiment with different value for So for the leading car. Try the find the value that allows the trailing car to reach its maximum distance before its graph intersects the leading cars graph, in other words before the trailing car SMASHES INTO the leading car.

  6. Calculate the time that corresponds to the trailing car covering that distance at 35 mph. This is the time separation you need to safely follow a car at this speed.
  7. Use a highway velocity, like 70 mph, and calculate the safe distance and time separation needed.