Radicals in Applications

Problem 196: The skid marks of a vehicle involved in an accident were 122 feet long. The speed of the car before the brakes were applied is $\sqrt{24d}$ feet/second. Find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Solution: Let $s$ be the speed of the car. Then

(1) $\begin{align*} s & = \sqrt{24d} \\ & = \sqrt{24 \cdot 122} \\ & = 54.1109970339 \\ & \approx 54.1.\end{align*}$

Hence, the speed of the cards before the brakes were applied was 54.1 miles per hours.

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