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Speed (within distance) problem, traffic related!

  1. Nov 22, 2011 #1
    Hello! I,m wondering if someone can help me out with a speeding ticket problem!! Here,s the scenario (or the question, if you will...) The passing lane is exactly 550 feet long....MY question is....how SLOW would a car have to be going if ANOTHER car was to pass the first car, within that 550 feet passing lane, WITHOUT exceeding 55 miles per hour....I,m trying to illustrate to the judge that, within that very short passing lane, that for a car to pass another car WITHOUT GOING FASTER THAN 55 MILES PER HOUR, THE CAR BEING PASSED WOULD HAVE TO BE GOING QUITE SLOW...ANY help would be greatly appreciated! Thanks in advance! Jeff
     
  2. jcsd
  3. Nov 22, 2011 #2
    Hi Jeff,

    Welcome to Traffic Court Forums. Whoops, Physics Forums.

    Haha, joking aside, I need to know 2 things to find this answer. I need to know how far apart the two cars start off, and I need to know the speed of the first car if i assume the second car travels at 55mph.
     
  4. Nov 22, 2011 #3
    HEllo and thanks for responding! I was DIRECTLY behind the car being passed...as far as HIS speed, I truly don,t know...what I,m trying to determine is what speed (ie how SLOW) a car would have to be going for another car DIRECTLY behind him at the start of a 550 foot long passing lane to pass that first car WITHIN the 550 feet, WITHOUT going over 55 miles per hour..I imagine this is some sort of vector equation, but beyond my VERY limited mathematical scope!..Thanks! Jeff
     
  5. Nov 22, 2011 #4
    ..PS...I suppose for all intensive purposes, you could have both cars side by side at the start of the 550 feet passing lane...might make the math a wee bit easier...thanks! ( by the way, my whole contention in this situation is that to actually PASS someone within 550 feet, without breaking a 55 mph speed limit, the PASSED car would have to be going quite slow...and this is WITHOUT the added pressure of ANOTHER car coming AT you the opposite way! ( the policeman in this particular instance suggested that I could have crashed head on into the oncoming traffic, but at least then I wouldn't have exceeded the 55 mph limit, and hence broken the law!
     
  6. Nov 22, 2011 #5
    From the sounds of this, I don't have enough information. Are you simply asking me (assuming a length of say 12 feet for a car), how much faster would a car behind that car have to be going to pass it in 550 feet? I can do that problem for you, but I don't really understand its significance.

    Maybe if you draw a little diagram you will be able to help me in understanding the situation .
     
  7. Nov 22, 2011 #6
    ...don't know how to draw a diagram on line...sorry! But, as answer to your quedstion, no...what I,m trying to determine is the MAXIMUM speed of car #1 (the one BEING passed) for ANOTHER car (..the PASSING car, car #2), starting at the SAME point at the start of a 550 feet long distance, to pass WITHIN that distance WITHOUT going over 55 mph to do it...
     
  8. Nov 22, 2011 #7
    It will take roughly 6.8 seconds for a car at 55mph to travel 550 feet. A safe passing distance if both cars start with their back wheels at the same distance is probably 20 feet. The slower car will travel 20 feet less after 6.8 seconds by being 3 feet per second slower. Therefore the maximum speed of the slower car will be 53 mph. (3 feet per second is 2 mph)
     
  9. Nov 22, 2011 #8
    Thanks so much for working that our for me! That will (I HOPE!) help greatly in my expanation to the court! (In a nutshell, I went to pass a car in a passing lane that is 550 feet long...the car I was passing was going (I estimate) about 48 miles perhour...and there was no one coming in the opposite direction...right after I pulled out to pass and was pretty much even weith the other car, a car pulled out of a driveway headed right at me! So I sped up (rather than slamming on my brakes and possibly skidding all over the road) to 70 mph to safely pass within the 550 feet passing lane (AND of course without having a head on collision with the now-oncoming car!)...Police wrote me a ticket for 70 in a 55 mph zone...and when I reminded him of the all-of-a-sudden-oncoming car, and wanting to avoid a head on collision, he suggested that at least then I wouldn't have gotten a speeding ticket! So then I "suggested" to him that I found it hard to believe that HE (or anyone ELSE, for that matter) had perhaps at one time or another found themselves in a passing situation where a danger came up, and one had to perhaps exceed 55 just to stay ALIVE!)...and of course, that was like talking to a brick...anyway, I,m going to present my case today at 1:00 to the local town court...just wanted to be armed with all pertinent injfo...thanks again! MUCH appreciated (though in reality, I don't expect much satisfaction!) Regards and thanks...Jeff
     
  10. Nov 22, 2011 #9
    :) no problem. I hope that it works out for you.
     
  11. Nov 23, 2011 #10
    Let’s make some assumptions:
    1) For brevity, let’s call the passing lane, “PL”
    2) The average length of a car is 15 feet, so assume both cars are 15 ft long
    3) You begin making your pass just after your car is completely within the PL
    4) You finish making your pass just before the end of the PL
    5) You travel at a constant rate of 55 mph while you are within the PL
    6) The other car travels at a constant rate while you pass it
    7) You begin passing when you are 10 feet behind the other car
    8) You finish passing when you are 15 feet ahead of the other car

    Since your car is fully within the PL before you begin passing, that means your rear bumper has just entered the PL. Therefore, your front bumper is 15 feet into the PL. You finish passing the car just as your front bumper reaches the end of the PL. So, the total distance you travel while making the pass is 550 ft – 15 ft = 535 ft.
    55 mph equates to approximately 80.7 feet per second, so it would take you 535 ft ÷ 80.7 fps = 6.6 seconds to make the pass.

    For you to meet all of the assumptions listed, the second car would travel (at most)
    550 – 15 (length of your car at beginning of PL) – 10 (the distance behind the other car when you begin) – 15 (distance of other car from rear to front bumper at beginning of pass) – 15 (distance ahead of other car that you finish pass) – 15 (length of your car at end of PL)
    = 550 – 15 – 10 -15 -15 -15 = 480 ft.

    Since the other car travels that distance in the same time, it would be traveling at 480 ft ÷ 6.6 = 72.4 fps, or about 49.3 mph

    So if you passed at a constant speed of 55 mph, the other car would be traveling at a maximum constant speed of 49.3 mph within the passing lane. That’s making maximum use of the passing lane. If you passed legally (taking reaction time and acceleration into effect), with the other car only doing 48 mph (as you estimated), you would NOT have had enough room to pass. In other words, you would have had to speed to complete the pass within the PL.
     
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