Rods, frames and coils in code

You will write three functions for the problems of this lesson.

The idea. A falling rod on rails has the terminal speed $v_t = \dfrac{mgR}{B^2l^2}$. A square frame that crosses a field makes the heat $Q = \dfrac{2B^2a^3v}{R}$. A coil in series with a battery has $I = \dfrac{\mathcal{E}}{R}\left(1 - e^{-t/\tau}\right)$ with $\tau = L/R$.

Your tasks.

1. In terminal_speed, return the speed in m/s of a rod of mass mass in kg, length length in m, in a field field in T, with a circuit resistance resistance in ohm. Use $g = 9.8\ \text{m/s}^2$.
2. In frame_heat, return the heat in J made in the whole crossing of a square frame of side side in m.
3. In lr_current, return the current in A at the time t in s after the switch is closed.