Can You Avoid a Speeding Ticket with a GPS Tracker?

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AI Thread Summary
To avoid a speeding ticket with a GPS tracker while driving to Sandy Springs, the maximum average speed must be calculated based on the total distance and time constraints. The driver has already traveled 46 km at a constant speed of 80 km/h, which affects the average speed for the entire trip. The key is to determine the speed for the last segment of the trip without exceeding an average speed of 100 km/h over one hour. By calculating the time spent at 80 km/h and the remaining time for the last 46 km, the maximum allowable speed can be derived. The solution emphasizes that while speeding is possible, the average speed must remain below the legal limit to avoid detection.
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Homework Statement


Due to several previous unfortunate encounters with law enforcement, your car has been equipped with a GPS tracking device. You know that this device radios your current position to police headquarters at precisely hour intervals, but you don't know the exact time at which this occurs (i.e. it could be every hour on the hour, or every hour on the quarter hour, or something else). If the police can prove that you've driven faster than 100 km/hr at any point, then you are busted.

You have been driving from State College to Sandy Springs, Utah (the latest hot Spring Break destination) along a perfectly straight road for several hours at a leisurely constant speed of 80 km/hr. Sandy Springs is only 46 km ahead. You realize that you can now speed up for the remainder of the trip, without getting busted.

What is the maximum average speed at which you can finish the drive to Sandy Springs, with no chance of getting busted by your GPS tracker?



Homework Equations



At first, I tried using d = 1/2 (v0 +v)t since we don't know the acceleration. But we don't even know the time, so I tried using v^2=v0^2 +2ad, but we still don't know the acceleration. I'm starting to think that this problem requires more than 1 kinematics equation. But I don't know which ones. Can someone please help me?



The Attempt at a Solution



No idea.
 
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well, can vf be considered 100km/hr?
 
No complicated formulas here, just average speed. Worst case is that they check your speed just as you arrive. So you go at some velocity V for 46km. Takes time T=46km/V. The rest of the hour (1-T) was at 80km/hr. Compute an average speed for the last hour of the trip and see how big V can be before the average speed exceeds 100km/hr. I'm giving you more than the average number of hints since you have another kind of speed problem. Good luck in the 40min.
 
dukiex3 said:
well, can vf be considered 100km/hr?

That's a guess, right? No, you can go faster. Not that I advocate violating the law.
 
Average speed over 1 hr <100km/h

If it drove at v for the last 46km... what's the time for the last 46km... the rest of the hour it was driving at 80km/h

Use (total distance)/(1 hr) = average speed <=100

solve for v.
 

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