An object weighing 1000 pounds sinks in water starting from rest. Two forces act on it, a buoyant force of 200 lb and the resisting force of water equal to 100v pounds, where v is in feet per second. If the acceleration due to gravity is considered to be 32 ft/s2. Determine the position of the object at any time t, with t in seconds. 16 128 I"(t) +(0 : 5 x(0) = 0 r'(0) = 0 (a) Determine, using only higher-order linear differential equation solving techniques, the solution to initial value problem.

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