Problem: Suppose Usain Bolt, running at a uniform speed of 9.0 m/s gives Lonesome George, crawling at a uniform speed of 0.9 m/s a head-start of 8.1 metres. How long will it take Bolt to catch up with George?
Solution 1: Bolt has 8.1 metres to make up, and his speed exceeds George's by 8.1 m/s. So it will take him exactly 1 second.
Solution 2: Bolt takes 0.9 seconds to get to where George was, by which time George has gone a further 0.81m. Bolt takes 0.09 seconds to get there, by which time George has gone another 0.081m. It will take another 0.009 seconds to make up that ground, and so on. It all adds up to precisely 0.999... seconds.
The point of bringing up this example is to get the "when" out of the debate. Most of you seem to have mental block because the equation is contingent on what is apparently a never-ending process. Well, here is something that lasts exactly 1=0.999... seconds, plus however long it takes you to understand the explanation.
Solution 1: Bolt has 8.1 metres to make up, and his speed exceeds George's by 8.1 m/s. So it will take him exactly 1 second.
Solution 2: Bolt takes 0.9 seconds to get to where George was, by which time George has gone a further 0.81m. Bolt takes 0.09 seconds to get there, by which time George has gone another 0.081m. It will take another 0.009 seconds to make up that ground, and so on. It all adds up to precisely 0.999... seconds.
The point of bringing up this example is to get the "when" out of the debate. Most of you seem to have mental block because the equation is contingent on what is apparently a never-ending process. Well, here is something that lasts exactly 1=0.999... seconds, plus however long it takes you to understand the explanation.
In fact, he is faster than the force of gravity! (9.9m/s)
So its actually 9.8 m/s^2
