# M8.4.11

**rate of change of one variable**is dependent on how much there is of another variable (e.g., the rate of change of speed is proportional to the amount of force acting on it).

### Why Tailgating on Freeways is Unsafe: A Real-life Example Using Quadratic Equations

We discuss how to compute the stopping distance of a car traveling at a given speed-- a real life application of a math topic, quadratic equations, and science topics, such as motion, kinetic energy, and work done. We also discuss the idea that while mathematics can be utilized to model real life situations, there is much more to consider, if one wants more refined and appropriate solutions to real life problems.

### Water Bottles, Root Beer, and Air

The common plastic water bottle makes a useful container for demonstrating properties of gases and liquids. As typical examples, we know that "air" is a gas (made up of nitrogen, oxygen, water vapor, ozone, carbon dioxide, and several "trace" gases) and water is a liquid. We should also note that gases and liquids are both "fluids". That is, they can flow or change shape, rather than having a fixed shape like a solid.