Police Problem

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 [itex] a = -32 \frac{ft}{sec^{2}} [/itex]. So [itex] v_{x}^{2} = v_{x}_{0}^{2} + 2a_{x}(x-x_{0}}) [/itex]. Since [itex] v_{x} = 0 [/itex], [itex] 0 = v_{x}_{0}^{2} - 64(19.2) [/itex]. So [itex] v_{x}_{0}^{2} = 1228.8 [/itex] and [itex] v_{x}_{0} = 35 [/itex]. So he was speeding. Is this correct?

Thanks

 

[itex] v_{x}_{0} = 35 \frac{ft}{sec}[/itex]. Is this correct?

Thanks

 

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