write in python code

In class you learned that the ODE describing the velocity gained by a falling body is om (1) c du dt (1 - 0) For a body of mass m, acceleration of gravity 9, and drag coefficient c. The closed form solution of the equation is gm v(t) = (1 - e-le/m)) = vr(1 e-c/m) (2) where vr is the terminal velocity. We also learned in class that the velocity of the ball can be iteratively calculated by numerically solving the ODE using the formula m vti+1) = v(ti)+(9-(t)At = v(t) + (9-pingut(+1 4) where v(t+1) is velocity of the body at time ti+1, and v(ti) at time to. At is size of the time-step, and the above equation works for a small enough time-step size. Write a program to calculate the velocity of the body at different time, as it accelerates to it's terminal velocity, using equation (3). You can assume g = 10, m= 10 and c = 50. (a) Plot the variation of velocity in time. (b) What is the maximum time-step size At that allows accurate calculation of the velocity (@) Will the maximum allowable time-step size At change if the mass of the body (m) increases to m=100? (d) Theoretically, the falling body will take time t = o to reach terminal velocity (ur). Using the program, calculate the time required by the body to attain 99.99 percent of the terminal velocity (ur)