Question

Accident investigation: The skid marks for a car involved in an accident measured 216 feet. Use the formula $\mathit{s}\mathbf{=}\sqrt{\mathbf{24}\mathbf{d}}$to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

Short answer

The speed of the car was 72 miles per hour.

Step-by-step solution

Step 1. Given Information:

The skid marks of the accident measured around 216 feet,

Formula :$\mathit{s}\mathbf{=}\sqrt{\mathbf{24}\mathbf{d}}$

Step 2. Assign the value to the equation:

Let s be the speed in the formula,

d is the given distance,

Substitute in the given information in the formula :

$$\begin{gathered} \mathit{s}\mathbf{=}\sqrt{\mathbf{24}\mathbf{d}} \\ \mathit{s}\mathbf{=}\sqrt{\mathbf{24}\mathbf{\left(}\mathbf{216}\mathbf{\right)}} \\ \mathit{s}\mathbf{=}\sqrt{\mathbf{5184}} \\ \mathit{s}\mathbf{=}\mathbf{72}\mathbf{}\mathit{m}\mathit{p}\mathit{h}\mathbf{.} \end{gathered}$$

Step 3. Checking the solution: 

Here speed s = 72,

$$\begin{gathered} \mathit{s}\mathbf{=}\sqrt{\mathbf{24}\mathbf{d}} \\ \mathbf{72}\mathbf{=}\sqrt{\mathbf{24}\mathbf{d}} \\ \mathbf{72}\mathbf{=}\sqrt{\mathbf{24}\mathbf{\left(}\mathbf{216}\mathbf{\right)}} \\ \mathbf{72}\mathbf{=}\sqrt{\mathbf{5184}} \\ \mathbf{72}\mathbf{=}\mathbf{72}\mathbf{}\mathit{m}\mathit{p}\mathit{h}\mathbf{.} \\ \mathit{h}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{d} \end{gathered}$$