Question 1 a) The time rate of change of a falling object's height can be given by the differential equation where y = height of the object, a = acceleration and t = time. An object is dropped from a height of 500m, with an acceleration due to gravity of -9.8m/sec², (i)Express the height of the object as a function of time. (ii) When will the object reach ground level? b) The acceleration (a =) of a car can be shown to obey the following linear differential equation = 0.05(250-v), where v is the velocity of the car. (i) Express the velocity of the car as a function of time. (ii) How long does it take the car to accelerate from rest to 200km/h? c) Find the general solution of d'r dr ds² ds - 2r=0 d) Find the first four non-zero terms of the power series solution for the differential equation y" + x²y = 0.