The velocity, , of an object moving through a fluid can be modeled by the drag equation = 2 where is a constant. An object moving through the water has an initial velocity, 0, in the interval of 16 m/sec 0 20 m/sec. After 2.0 seconds, the velocity has decreased to 1 in the interval of 8 m/sec 1 12 m/sec.

a. Find the equation that models the velocity of the object, at any time, (choose a value of 0 and 1 from the given intervals). By using an appropriate analytical method, solve the derived model, explain the reason for the selection of the method and discuss the behavior of the velocity, () for interval of 0 10 and approaches to infinity.

b. Compute the velocity of the object after 10 seconds by using the derived model in Part 1(a) with TWO (2) different numerical methods with step size, = 2 seconds. Select the best numerical method to compute the velocity of the object and justify your answer by computing the percentage of relative error.