Car crash

A car crash occurred on the road with a maximum permitted speed of 60 km/h. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, assuming a decelerated motion of the vehicle with a deceleration of 5 m/s²

Correct answer:

s =  27.7778 m

Step-by-step explanation:

$$\begin{gathered} s_1=40\text{m} \\ a=5{\text{m/s}}^2 \\ v=60\text{km/h}\to \text{m/s}=60:3.6\text{m/s}=16.66667\text{m/s} \\ t=v/a=\frac{50}{3}/5=\frac{50}{3\cdot 5}=\frac{50}{15}=\frac{10}{3}\doteq 3.3333\text{s} \\ s=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot 5\cdot {\frac{10}{3}}^2=\frac{250}{9}\doteq 27.7778\text{m} \\ {s}_1>s \\ v>60\text{km/h} \end{gathered}$$

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