# What Can Mathematics Tell Us

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1 What Can Mathematics Tell Us about Bicycle Accidents? By Jen and Lorenzo Period 4

2 What affects the severity of a bicycle crash?

3 Who or what impacts harder: A child, teen, or an adult? A fast bicycle or a slow bicycle?

4 Momentum is used to measure motion (and the resulting impact). Momentum = mass x velocity M = mv

5 To determine if a child or an adult impacts hardest, substitute various weights in the momentum equation and solve it for a constant speed. For example, if the speed is 10 mph then the equation becomes M=10m The domain is the set of all possible rider weights.

6 Weight to Momentum Table Weight Speed Relative Momentum Child 50 lbs 10 mph 500 lb mph Teen 100 lbs 10 mph 1,000 lb mph Adult 150 lbs 10 mph 1,500 lb mph

7 What the Weight to Momentum Table Tells Us If the domain is 50 to 150 lbs, then the range is 500 to 1,500 lb mph. For a given speed, the momentum increases with the weight of the bicyclist. An adult impacts harder than a child.

8 To determine if a fast bicycle or a slow bicycle impacts hardest, substitute various speeds in the momentum equation and solve it for a constant weight. For example, if the rider weighs 100 lbs, then the equation becomes M = 100 v The domain is the set of all possible bicycle speeds.

9 Speed to Momentum Table Weight Speed Relative Momentum Teen 100 lbs 5 mph 500 lb mph Teen 100 lbs 10 mph 1,000 lb mph Teen 100 lbs 15 mph 1,500 lb mph

10 What the Speed to Momentum Table Tells Us If the domain is 5 to 15 mph, the range is 500 to 1,500 lb mph. For a given weight, the momentum increases with the speed of the bicycle. A fast bicycle impacts harder than a slow bicycle.

12 What the Chart Tells Us For a given weight, the momentum increases with the speed of the bicycle. A fast bicycle impacts harder than a slow bicycle. Adults impact harder than teens, and teens impact harder than children. The more weight, the harder the impact.

13 Extending to Everyday Living Does this analysis answer the question, Is it as important for an adult to wear a bicycle helmet as it is for a child?

14 Wearing Bicycle Helmets As I have shown, an adult impacts even harder than a child. Therefore, it is at least as important for an adult to wear a bicycle helmet as it is for a child. More than 20 states and 87 localities in the United States, all of Australia, and parts of Canada require bicycle helmets.

15 For more information see: Bicycle Helmet Safety Institute Citizens for Safe Cycling Bike Tricks, Stunts, and Bones htm

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