# Traffic collision

When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village before braking?

Result

v =  72 km/h

#### Solution:

$s=150 \ \text{m} \ \\ t=15 \ \text{s} \ \\ s=at^2/2 \ \\ a=2 \cdot \ s / t^{ 2 }=2 \cdot \ 150 / 15^{ 2 } \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \text{m/s}^2 \ \\ v_{1}=a \cdot \ t=1.3333 \cdot \ 15=20 \ \text{m/s} \ \\ v=3.6 \cdot \ v_{1}=3.6 \cdot \ 20=72 \ \text{km/h} \ \\ v>50 \ km/h$

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