She have a J2 Rocket strapped to the back :rofl:
https://nrich.maths.org/discus/messages/8577/7263.html?1071520520Here's some good math for you on this thread :)
Hello,
I received a speeding ticket the other day and to build my defense I need the following information and do not possess the mathematical ability to figure this out. Could anyone please help me? I was cited for going 41 MPH in a 25 MPH zone. The officer said that he picked me up on his radar going 41 MPH almost immediately after I came to a stop and preceded. I probably advanced less than 50 feet before he clocked me at 41 MPH. I want to show the judge that it would be impossible to reach a speed of 41 MPH in such a short distance. I know this about my car which is a 1992 Honda Accord. It goes 0 - 60 MPH in 9.8 seconds. It does the 1/4 mile in 17.4 seconds. So with that we know that the car can averages 75.86 FT per SEC at 9.8 SEC to go 0-60 MPH and we also know that the car traveled 743.45 FT to reach 0 - 60 MPH in 9.8 seconds. What I want to know is how many feet would the car have to travel to reach a speed of 41 MPH and if possible how many seconds would it take. I know we are probably missing some acceleration info here, but anything logical and close that I could show or prove to the judge with math would be a great help for my defense. I am not guilty and the officer refused to show me his radar reading to prove to me I did this. Thanks
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60 MPH = 88 feet per second.
So the acceleration in feet per second is 88/9.8 = 8.98 ft/s2.
In most cars, the acceleration is not constant over the range 0-60 MPH, but if it were then you could solve the equation
50 = (8.98/2)t2
to find the time, t, it takes the car to reach the 50-foot mark. That time is about 3.3 seconds. In 3.3 seconds, your speed reaches 8.98*3.3 = 30 feet per second, or about 20.4 MPH.
While you have the accelerator pedal fully depressed, a Honda Accord stays in first gear until about 40 MPH, and so the acceleration is much higher than the average over 60 MPH. But the acceleration would have to be greater than that of gravity for you to reach 41 MPH in just 50 feet. If the cop was right, and if you really stopped at that stop sign (you did stop, right?) then you would have gone from zero to 41 in just 1.66 seconds -- quite an exhilarating ride!
If you can prove that your speed was clocked just 50 feet from the stop sign, and you can prove that you stopped at that stop sign, then you can prove that the acceleration your car experienced during that 50 feet far exceeds the capacity of a standard Honda Accord. Here are the equations:
Let a be the acceleration, in feet per second, of your car.
Let t be the time, in seconds, that elapsed from the stop sign to the 50-foot mark, where you were going 41 MPH, or 60.1333 ft/s.
These two equations relates a and t, given that you accelerated smoothly from 0 to 60.1333 ft/s, and traveled 50 feet doing so:
(1) 50 = (a/2)t2
(2) a = 60.1333/t
Since you were in first gear the whole way, and the torque generated by the Honda Accord is fairly constant over that range, the smooth acceleration is a reasonable approximation.
Substituting 60.1333/t in place of a in the first equation, we get
50 = 30.0667t
so t = 1.66 seconds
From the second equation, we find a = 60.1333/1.66 = 36.16 ft/s2, which is quite a bit greater than the acceleration of a Honda Accord.
Now, as a practical matter, you may find it difficult to prove that the reading was taken just 50 feet from the stop sign -- that's probably no more than the width of the street you crossed. If the reading were taken, say, 50 yards instead of 50 feet from the stop sign, then your whole case is toast. I think you stand a much better chance of acquittal if you argue that the cop didn't take a measurement of your car at all. Your evidence is that he did not show you the reading. Good luck!