Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity v, so that dv=dt D "kv2. Show that v. t / D v0 1 C v0kt and that x. t / D x0 C 1 k ln.1 C v0kt /: Note that, in contrast with the result of Problem 2, x. t / ! C1 as t ! C1. Which offers less resistance when the body is moving fairly slowly—the medium in this problem or the one in Problem 2? Does your answer seem consistent with the observed behaviors of x. t / as t ! 1?