Studying the Task for Speed - Assignment Example

Zeno argued that Achilles would continually gain on the tortoise, but he would never reach him. Was his reasoning correct? If Achilles were to pass the tortoise, at what point of the race would it be? Based on the statement of the paradox, let x = the speed of the tortoise so that 10x = the speed of Achilles. Also, while the tortoise covers the distances 1000 m, 1100 m, and 1110 m each of which corresponds to the instant at which Achilles covers from 0 to distances 1000 m and 1100 m, one observes that the tortoise takes on a sequence of displacement in decreasing order as shown in its capacity to move across a 1000 meters then the next 100 m, then 10 m, that this creates a decreasing pattern where the next elements can be estimated to be 1, 1/10, 1/100, 1/1000 and so on.

However, though the tortoise appears to move with less and less of a span travelled, Achilles would have to work on filling in steps or strides to be able to catch up with it – something which tends to be impossible for each task he takes is simply part of an ‘infinite’ number of tasks he is yet to carry out and every time, the tortoise would have gone a bit farther. Thus, Zeno’s argument may be claimed to have been justified as correct in reasoning through such a scenario. About their rates, if Achilles were to catch up with the tortoise at 10 times the animal’s rate at some time, t, then 10x*t = x*t + 1000.

Solving this equation for distance ‘xt’, 9xt = 1000 and xt = 111 and 1/9 meters or that about 111.11 meters must have been taken by Achilles to overtake the tortoise. The figure likely expresses a representation of a finite value to which the partial sums 100, 110, 111, etc. converge.