Question

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 at ground. As a further simplication, 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 Fd = dv2 , draw a free body diagram of the bike and show that velocity can be modelled with

the ODE:

dv

dt

+

d

m

v2 = 0:

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

dt

+

20d

m

va =

100d

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?

Answer 1