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Bill, George, --> near miss .... or nearly missed



George is driving 100 ft/sec toward an intersection. He looks to his right, and sees Bill, driving 30 ft/sec toward the same intersection. George foolishly slams on his brakes. If he had kept going 100 ft/sec, he would have been through the intersection long before Bill got there. At the instant that he slams on his brakes, the center of George's car is 125 ft from the intersection, and the center of Bill's car is 150 ft from the intersection. George's brakes give his car an acceleration of -30 ft/sec/sec. Bill never changes his speed. Each car is 13 ft long and 7 ft wide.
Will there be a collision?
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At t=2 seconds, George's speed will be 40ft/s. Since his acceleration is constant, his average speed from t=0 to t=2 is (100+40)/2 = 70ft/s. Hence he will have traveled 140 feet in the first two seconds. The center of his car will be 15 feet past the intersection, which puts the rear of his car 8.5 feet past. Even if George stopped completely at this point, he would be in the safe zone since Bill's car only sticks 3.5 feet out from the line traveled by its center. Bill will only have traveled 60 feet in this time, so he is still far from reaching the intersection. No collision.

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