I have been asked about the math behind the Justice Question:
The data I use is off a website somewhere.
The Celica accelerates at 8 mi/h/s which is 28 800 mi/h/h ( a = 28 800)
Therefore to go to 62 mph would take 7.75 seconds. (using integration then converting time from hours into minutes) (v = 28 800t) and to go to 45 mph it would have taken 5.6 seconds.
D = 14 400 t ^2 The distance covered in 7.75 seconds is 0.066 miles or 352 feet to get to 62 mph from 0, and 184 feet to get to 45 mph from 0. 168 feet to go from 45 mph to 62 mph.
This shows it is POSSIBLE for the car to accelerate to 62 mph in the 400 feet stated in the article, IF the driver accelerated at the cars maximum acceleration, and there were no vehicles in front of it impeding its speed.
The car had traveled 1980 feet in 30 seconds. The average velocity is 45 mph. For an average to be 45, and he was stopped at one point then he would have had to be traveling OVER 45 mph at some point.
For the average speed to be 45 mph, the area below 45 must be equal to the area above 45 on a V-T graph.
Assuming acceleration and decceleration are equal, to accelerate from 0 - 62 then back down to 45, would have taken a total of 520 feet with 152 ft MORE above the graph, and 9.9 seconds. Thefore he must have slowed down below 45 mph. He could have drove down as far as 10 mph and back up.
This shows it is quite possible he was speeding.
In my class, due to the math of each side I made the ruling of NOT GUILTY. I made the ruling based on the arugements of my students not the actualy math.
Some students made calculation mistakes, for which the other side criticized.
Hi Dave,
ReplyDeleteI love your stuff and I love this activity in particular. I'm planning to use it with my Math 31 class in the next couple of weeks.
I think you've made a mistake in your interpretation of the article. (Or else I have). I think the 400 ft number mentioned in the article is a general location of where this incident took place. My interpretation is that the second GPS ping happened at the same location as the radar measurement: 1980 feet from the Freitas Road intersection. I don't think the 400 ft number comes into the problem at all.
Thanks again for the great teaching idea and please let me know if you disagree with my interpretation.