Did Police Make the Right Call in Speeding Arrest Based on Skid Mark Length?

[courtrigrad]

The question is whether a driver is exceeding a 30 miles/hr speed limit before he makes an emergency stop. The length of the skid marks on the road is 19.2 feet. The police assumed that the maximum deacceleration of the car would not exceed the acceleration of a freely falling body and arrested the driver for speeding. Was this correct to do?

So the acceleration of a freely falling body is $a = -32 \frac{ft}{sec^{2}}$. So $v_{x}^{2} = v_{x}_{0}^{2} + 2a_{x}(x-x_{0}})$. Since $v_{x} = 0$, $0 = v_{x}_{0}^{2} - 64(19.2)$. So $v_{x}_{0}^{2} = 1228.8$ and $v_{x}_{0} = 35$. So he was speeding. Is this correct?

Thanks

 

[Tide]

Be careful with your units! You used 32 ft/s^2 for the acceleration and 19.2 feet for the distance. What are the units of v? :)

 

[courtrigrad]

$v_{x}_{0} = 35 \frac{ft}{sec}$. Is this correct?

Thanks

 

[Tide]

So, was the driver speeding?

 

[courtrigrad]

no he wasnt. he was only traveling 23.86 miles per hour. I converted ft/sec to miles/hour.