During a lecture, we saw that if a particle of mass m is initially at rest at t0 = 0 and its initial position is xo = 0, and is subject to an exponential force F(t) = ma0exp (-bt) for t > 0 in the x direction, then its subsequent velocity is Vanalytical(t) = b/a0 (1 - e-bt).
Now, integrate numerically the ODE
mv = F
over a duration 5/b using the forward Euler method, splitting this time interval into 20 steps (i.e., Δt = 1/(4b)).
In what range does the value of |Vanalytical — Vnumncrical| fall at the end of the computational integration? (values displayed are in m/s)
Use the values a0 = 2 ms-2 and b = 0.1 s-1.
between 4 and 5 m/s
between 5 and 6 m/s
between 3 and 4 m/s
between 2 and 3 m/s
between 6 and 7 m/s