The braking distance d (in feet) of a certain car traveling v mi / hr is given by the equation d

step 1 In this problem, the breaking distance D with respect to the velocity V is given as D equals to

The braking distance d (in feet) of a certain car traveling...

The braking distance $d$ (in feet) of a certain car traveling $v \mathrm{mi} / \mathrm{hr}$ is given by the equation $d=v+\left(v^{2} / 20\right) .$ Determine the velocities that result in braking distances of less than 75 feet.

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Key Concepts

Domain Restrictions and Contextual Constraints

When solving real-world problems, it is essential to consider domain restrictions that come from the context. For example, physical scenarios may limit the acceptable range of solutions, such as excluding negative values when dealing with quantities like speed or distance, ensuring that the answer is practically meaningful.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation typically written in the form ax² + bx + c = 0. It can be solved using methods such as factoring, completing the square, or the quadratic formula, which makes use of the discriminant to determine the nature and number of the solutions.

Inequalities Involving Quadratic Functions

Solving a quadratic inequality involves first finding the roots of the corresponding quadratic equation to partition the number line into intervals. Then, by testing values from each interval, one determines where the quadratic expression is positive or negative depending on the inequality, which gives the range of values that satisfy the condition.

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