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/sec².
Bill never changes his speed.
Each car is 13 ft long and 7 ft wide.

Will there be a collision?

(In reply to Hey guys!! by FatBoy)

The problem was in using a constant negative acceleration for 4.67 seconds, rather than switching to zero acceleration at time =3.33 seconds as pointed out by fwaff's comment. That is the time (I'm assuming fwaff did the math) at which George's car came to a complete stop past the intersection. To plug 4.67 seconds into the original non-changing acceleration of -30 is to allow that the car then started to back up into the intersection. Presumable he would not do that. And even if he did, that would not be a near miss, but rather as he was going backward, would be entering the intersection (albeit from the opposite direction) and causing a collision.

Posted by Charlie on 2003-10-02 14:25:02