The braking distance (in meters) for a car with excellent...

The braking distance (in meters) for a car with excellent brakes on a good road with an alert driver can be modeled by the quadratic function $B(s)=.01 s^{2}+.7 s,$ where $s$ is the car's speed in kilometers per hour. (a) What is the braking distance for a car traveling 30 kilometers per hour? For one traveling 100 kilometers per hour? (b) If the car takes 60 meters to come to a complete stop, what was its speed?

The braking distance (in meters) for a car with excellent brakes on a good road with an alert driver can be modeled by the quadratic function $B(s)=.01 s^{2}+.7 s,$ where $s$ is the car's speed in kilometers per hour.
(a) What is the braking distance for a car traveling 30 kilometers per hour? For one traveling 100 kilometers per hour?
(b) If the car takes 60 meters to come to a complete stop, what was its speed?

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Key Concepts

Inverse Problem Solving

This concept involves determining the input value for which a function yields a given output. In mathematical modeling, this often requires solving an equation—frequently quadratic—to reverse-engineer the cause from the effect.

Solving Quadratic Equations

This technique is used to determine the values of the variable that satisfy a quadratic equation. Common methods include factoring, completing the square, and using the quadratic formula, which are critical for finding solutions in models that lead to quadratic relationships.

Quadratic Functions

These functions are polynomial expressions of degree two, typically written in the form ax² + bx + c. They are fundamental in modeling scenarios where the relationship between variables involves acceleration, deceleration, or other squared rates of change, leading to a parabolic graph.

Function Evaluation

This process involves substituting a specific input value into a function to obtain the corresponding output. It is a basic yet essential skill in applying mathematical models to real-world situations.

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