The differential equation governing the velocity of an object is
where k > 0 and n are constants. At t = 0, the object is set in motion with velocity v0.
(a) Show that the object comes to rest in a finite time if and only if n < 1, and determine the maximum distance traveled by the object in this case.
(b) If 1 ≤ n < 2, show that the maximum distance traveled by the object in a finite time is less than
(c) If n ≥ 2, showthat there is no limit to the distance that the object can travel.
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