The differential equation governing the velocity of an object is where k > 0 and n...

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.