Stopping Distances. The number of feet that a car travels...

Stopping Distances. The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance. For one driver, the stopping distance $d(v),$ in feet, is given by the polynomial function $d(v)=0.04 v^{2}+0.9 v,$ where $v$ is the velocity of the car in mph. Find the stopping distance at 60 mph. (IMAGE CANNOT COPY)

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Key Concepts

Modeling Physical Relationships

Modeling physical relationships involves using mathematical equations to represent how one physical quantity depends on another. In contexts like stopping distances, the relationship between speed and distance is often represented with functions that account for various contributing factors, such as reaction time and braking efficiency.

Polynomial Functions

Polynomial functions involve expressions where variables are raised to integer powers and multiplied by coefficients before being summed. They are used to model a variety of phenomena, including relationships where changes in one quantity do not produce proportional changes in another, as seen in many physical contexts.

Function Evaluation

Function evaluation is the process of substituting a specific input value into a function to compute the corresponding output. This is a fundamental concept in mathematics, allowing one to determine the function’s value for any given instance and hence solve practical problems.

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