Can You Avoid a Speeding Ticket with a GPS Tracker?

  • Thread starter mpgriffis
  • Start date
In summary, the conversation discusses how to calculate the maximum average speed for a car to reach a destination without getting caught by a GPS tracker. The person driving has been going at a constant speed of 80 km/hr for several hours and has 46 km left to reach their destination. The solution involves finding an average speed for the last hour of the trip and calculating it so that the total average speed over the entire trip is less than 100 km/hr. This can be done by setting up a formula with the total distance and time, and solving for the velocity.
  • #1
mpgriffis
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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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  • #2
well, can vf be considered 100km/hr?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 

1. How should I approach solving a problem due in 40 minutes?

The best approach is to start by understanding the problem and breaking it down into smaller, manageable parts. Identify the key information and any given constraints. Then, brainstorm potential solutions and choose the most feasible one to work on.

2. What should I do if I get stuck on a problem due in 40 minutes?

If you get stuck, take a step back and try to approach the problem from a different angle. You can also consult with classmates or your teacher for clarification or guidance. Don't be afraid to ask for help when needed.

3. How can I manage my time effectively when working on a problem due in 40 minutes?

Start by setting a timer for yourself to help you stay on track. Prioritize the different parts of the problem and allocate time accordingly. Don't spend too much time on one part and remember to take breaks to stay focused.

4. What are some common mistakes to avoid when working on a problem due in 40 minutes?

Some common mistakes include not reading the problem carefully, not double-checking your work, and not managing your time effectively. It is also important to avoid making assumptions and to show your work step by step.

5. How can I effectively check my work before submitting a problem due in 40 minutes?

After completing the problem, take a moment to review your work and make sure it aligns with the given instructions. Double-check any calculations or key information to ensure accuracy. If time allows, have someone else review your work as well.

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