Question

Question 9 You should be able to answer this question after studying Unit 8. An object moves along a straight line, and its speed v (in metres per second) when at a position r (in metres) from its starting point can be modelled by the differential equation 10 marks 0 dr0, 20), where k is a positive constant (a) Find the general solution of this differential equation in explicit form (b) The speed of the object at its starting point is 10ms-1. Find the particular solution that describes the speed of the object as a function of its position from its starting point. (c) The speed of the object is 20 ms-1 when it is 5m from its starting (d) Use your particular solution to calculate the position at which the speed e) Use Maxima to find the solution to the initial value problem 2 point. Find the value of k. 2 is 40 ms 0 where v(0) 10, =-, for a general value of k. Include a screenshot or printout of your Maxima worksheet in your answer. You may find that Maxima gives a solution in implicit form

Answer 1

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