Ticket or No Ticket?
Known Fact: The distance a speeding car takes to stop is directly proportional to the square of the car's speed when the brakes are first applied.
Police Report: In a 70 mph speed zone, the TurboChevy involved in an accident left skid marks that were 240 feet long. According to our data chart, a TurboChevy requires 170 feet to stop if it's brakes are applied at a speed of 60 miles/hour.
Question: What was the speed of the TurboChevy just before the accident?
Related Question of Interest: Suppose the speed of a car is doubled...what is the effect on the stopping distance (e.g. what is the stopping distance for 30 mph)?
Source: Adapted from Ethan Bolker's Using Algebra, 1983, p. 212
Hint: What is the general formula for a direct proportion, relating the stopping distance D to the speed v? Can you use the known data to find the constant of proportionality?
Solution Commentary: You should find that D = 0.047 V^{2}, and that the TurboChevy's speed was 71 mph.
When a car's speed is doubled, its stopping distance is quadrupled!
Now, how exact is all of this... Ask your local police force about the formulas they use....and how they take into account the type of car, road conditions, weather conditions, etc. Will this mathematical model stand up in court as viable evidence?
