Charlie decides to create a theoretical model of his riding velocity to test whether his watch is callibrated properly. To simplify the problem, Charlie decides to test the watch on flat ground. As a further simplification, Charlie decides to start their trial at 10 m/s and then let the bike coast (aka no external force). 1. Given drag force can be modelled with equation Fa = dv?, draw a free body diagram of the bike and show that velocity can be modelled with the ODE: dv d 2 = 0. dt m 2. If Charlie linearises the ODE about the initial velocity of 10 m/s, show that the approximate velocity, Va, can be modelled with the ODE: dva 100d 20d -Va m dt m 3. Solve the linearised ODE for va given m = 70 kg, d = 1. 4. Solve the original (non-linear) ODE for v given m 70 kg, d = 1. 5. Plot the solutions for both the linear and nonlinear ODES over the interval of one minute. Under what conditions does the linearised ODE accurately model velocity? Hint: You can adjust the y-axis limits of a plot using the ylim function.