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- Thread starter symanarts
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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.

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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! JeffHi 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.

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..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!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

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Maybe if you draw a little diagram you will be able to help me in understanding the situation .

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:) no problem. I hope that it works out for you.

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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

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