To do this we need the relation or in words, integration is just the reverse of differentiation. Therefore indeed integration, at least for the case of constant velocity, just states the answer or prediction for motion. Finally, let's apply the tools developed to a practical, indeed topical, problem, air traffic control. A second airplane is 20 km west of the airport, heading north. First, do it the commonsense way, like the first approach to the tortoise-hare problem.
Plane one takes a time to get to the collision point.
The time for plane two is , where s is the unknown speed which would produce a collision. This means Now let's do this over using relative velocity and relative displacement in two dimensions. In more dimensions, the result is exactly the same. If there are more planes, one just has to look at every pair of planes and make sure they are not on a collision course in the same way we have done for one pair. In class I discussed the tortoise-hare problem in terms of Hecht's five steps for solving a physics problem.