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?

Upon finishing this problem I noticed that few people included the displacements of both drivers on their way to figuring out the answer. Here goes:
You are trying to figure out time!
Start out with what you know: the displacement of Bill is delta x=150ft, the Vo or initial velocity of Bill is 30ft/sec. Since there is no acceleration in Bill apply delta x (displacement)=Vot. Solve for time and you get 5.00 seconds. Then take George's displacement which is 125ft. His Vo = 100ft/sec and his "decelleration" is -30ft/s^2. Plug this into the equation delta x=Vot + 1/2at^2 OR 125 = (100)t + .5(-30)t^2 Solve for t using a quadratic you get 1.6667 seconds and 5.00 seconds. You cancel the 1.6667 secs because even without braking George would have still taken 1.25 seconds to cross the intersection! (125ft=100(ft/s)t; t=1.25s) Here the cars length and width are negligible because had they been just tiny particles they would have collided at the intersection anyways being that they arrived there at the exact time. Both cars get to the intersection in exactly 5.00 seconds. SPLAT!

Posted by Vito on 2003-10-02 20:32:53