Question: You should be able to answer this question after studying Unit 8. An object falls and is acted on by its weight and air

You should be able to answer this question after studying Unit 8. An object falls and is acted on by its weight and air resistance. Its velocity v (in metres per second) at time t (in seconds) can be modelled by the differential equation dv dt = k(4g v) (0v 0), where k is a positive constant and g is the acceleration due to gravity. Take 9 = 9.8 ms-2 (a) Find the general solution of this differential equation in explicit form. (b) The initial velocity is 1 ms-1. Find the particular solution that describes the velocity of the object as a function of time. (c) The velocity of the object is 15 ms-1 after 1 second. Find the value of k. Give your answer correct to two significant figures. (d) Use your particular solution to calculate the time at which the velocity is 30 ms. Give your answer in seconds to two significant figures. (e) Use Maxima to find the solution of the initial value problem dv dt = - k(4g v) where v(0) = 1.

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