Question

feet per second and in miles per second 18 An object of mass m is moving horizontally through a medium which resists the motion with a force that is a func- tion of the velocity; that is, d's dv f(v) dt =m dt2 where v = s(1) represent the velocity and at time , respectively. For example, v(t) and s position of the object think of a boat moving through the water. (a) Suppose that the resisting force is proportional to the velocity, that is, f(v) = -kv, k a positive constant. (This model is appropriate for small values of v.) Let = So be the initial values of v and s vo and s(0) v(0) Determine v and s at any time t. What is the total distance = that the object travels from time t= 0? (b) For larger values of v a better model is obtained by sup- posing that the resisting force is proportional of the velocity, that is, f(v) was first proposed by Newton.) Let vo and So be the initial values of v and s. Determine v and s at any time 1. What is the total distance that the object travels in this case? to the square =- kv, k >> 0. (This model

Answer 1

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