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?

At constant speed, Bill reaches the intersection in 5 seconds
George's motion is governed by the equation
s=ut+at*t/2
125 = 100t - 15t*t
This simplifies to
3t*t -20t + 25 = 0
(3t-5)(t-5) = 0
At first the two positive solutions worried me. Then I realised that if the car continues to decelerate the speed will eventually become negative & the car will reverse. That happens after 5 seconds. The solution that interests us is t=5/3 seconds. This is when George reaches the junction, well before Bill. Consequently there is no collision.

Posted by Robin Routledge on 2003-10-09 17:12:05